The language of porosity: rational randomness by Vittoria Fusco

THESIS REPORT

The language of porosity: rational randomness VERSATILITY OF INNOVATIVE AND MODULAR CLAY GEOMETRIES Vittoria Fusco Tutor: Ruby Law

MArch AD Architectural Design Cluster RC5&6 The Bartlett School of Architecture 2017/2018

The Bartlett School of Architecture, UCL, 22 Gordon Street, London WC1H 0QB MArch AD Architectural Design Cluster: RC5&6 Theory tutor: Ruby Law Date of submission: 13 July 2018 Student name: Vittoria Fusco Student number: 17145593 Student email: vittoria.fusco.17@ucl.ac.uk

CONTENT

Abstract

Keywords

1. Introduction

2. Different scales of porosity 2.1 Microporosity and porosity of materials 2.2 Porosity in architecture 2.3 Porosity on an urban scale 2.4 Scalability of our architectural proposal

3. Different layers of porosity 3.1 The first layer 3.2 The second layer 3.3 Uniqueness of our design proposal

10 11 13 17 19

24 26 36 39

4. Porosity in a dualism of space and matter

5. Porosity as a process

5.1 Porosity as act of adding 5.2 Porosity as act of subtracting 5.3 Porosity as pattern

55 57 62

6. The boundaries of porosity

Conclusion

Outlook

References

List of figures

Fig. 0: Clay geometry fabricated with the slipcasting technique.

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

ABSTRACT

This thesis report has both a theoretical and pragmatic intent. It will disclose and explicate the nuances and relativity of the concept of porosity. Porosity is a ubiquitous feature, albeit surprisingly unpredictable in its ontological manifestations. The relativity lies in the physical dimensions of porosity, in its interactivity with external entities, in the evanescence of its limits, in the uncertain cognizance of its generating processes and the controversial interpretation of its essence. Yet, it represents, undoubtedly, an immeasurable source of beneficial usages, with advantageous consequences. Ergo, if appropriately investigated and controlled by means of the contemporary digital and parametric instruments and techniques, porosity could become an invaluable resource in the design and actualization of architecture. And this research has been carried out by implementing the porous architectural material par excellence: clay.

Keywords Porosity, clay, scalability, versatility, porous layers, parametric control, rational randomness, aesthetic value, feasibility.

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

INTRODUCTION

Interest in the exploration of nature, with its free forms and logical processes,

porous and allow fluids to pass through them, in different ways and levels.

has inspired architects throughout the

Clay is an interesting example of a porous

ages. Not only did they attempt to imitate

natural material and its implementation in

the biological morphologies of nature, in

our project research raises the material as

order to attain more organic architectural

the emblem of such a persistent, almost

geometries, but also tried to investigate the

obsessive, reference to nature.

underlying structures and mechanisms, to enhance the performances of buildings in

Naturalness should be also achieved

terms of durability, efficiency and structural

in the technological systems adopted,

stability.

nowadays, in architecture. This idea is

When thinking about the realm of living

inherently related to the contemporary

creatures and inanimate objects ascribable

issues

energy

consumption,

to the definition of Nature, there is a

environmental pollution, depletion of

characteristic, a physical property, which,

resources and overproduction of waste

although not immediate and noticeable to

caused by the building industry. Hence,

the humanâ&#x20AC;&#x2122; mind, is, in reality, ubiquitous:

this report aims at proposing an innovative

porosity. In fact, all elements in nature are

and sustainable natural system intended 6

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

to guarantee the health and quality of the

efficiency and innovation.

indoor microclimate: a clay porous wall.

The functional scope, in this report and,

More specifically, through a series of

more in general, in the design research

examples of the manifestation of porosity

will always run parallel the pursuit of the

on different scales, Chapter 2 and 3 will

beauty of randomness. This will be sought

illustrate how the language of porosity

through the proposition of a revolutionary

has considerably pervaded our design at

language of modular clay components and

all levels and dimensions. The harmonic

the exploration of different manipulating

integration of different porous layers and

parametric strategies which ensure the

the scalability of our proposal will appear

coexistence of aesthetic fascination,

as essential and advantageous qualities. In

Fig. 1.1: Proposal for an architectural application of our modular and porous clay language.

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Chapter 4, a speculative and ontological

5. The evolution of the digital design

argumentation around the topic of the

process and the studied technological

perception of porosity and its influence

solutions which addressed the evidence of

on our design will resemble the dialectical

the feasible application of our innovative

debate of void and matter, with multiple

language to the real architectural world,

philosophic and scientific references.

will be explained in detail. Finally, the last

The technical challenges faced in the

Chapter will debate the controversial and

research of the parametric control of the

intellectual concept of the boundaries as

generating and changing processes of

a limit of a porous architectural language,

porosity, depending on external factors,

and, at the same time, its concrete

will be extensively described in Chapter

implications in the design proposal.

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

DIFFERENT SCALES OF POROSITY

Porosity is the quality of a certain material

different classes of stones. Human skin is

being porous, full of minute holes which

entirely covered with millions of pores,

allow liquid or gas to pass through it[1]. If

which guarantee its health by assimilating

we reflected more meticulously, for certain

air and good substances, and expelling air

we could assert that, in nature, everything

and oil that help protect it from the bad

occurs due to the porous property of

ones. No natural element, organism or

materials and organisms. Plants fulfil the

entity exists without interacting physically

photosynthesis process through pores,

and

called stomata, which permit the gas

elements, organisms or entities. And this

exchange, absorbing Carbon dioxide

interchange of matter occurs through

(CO₂) from the air and releasing oxygen

micro-voids contained in the molecular

(O₂)[2]. Various levels of porosity typical of

structure of all natural materials.

chemically

with

other

natural

stones affect the absorbance of disparate chemical substances, which causes the configuration, and distinction of the

[1] Houghton Mifflin Harcourt Publishing Company. 2011. Origin of porosity. [online]. Available from: http://www. dictionary.com/browse/porosity [Accessed 26 April 2018] [2] Paet Joseph Martin. 11 December 2010. Plant tissues and organs. [online]. Available from: http://www.dictionary. com/browse/porosity [Accessed 18 June 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

2.1 Microporosity and porosity of materials Porous materials are classified as low porous, middle porous or high porous depending on the number of the pores[3]. The pores, based on their size, can be distinguished as micropores, mesopores or macropores ranging from less than 2 nm to more than 50 nm. They can be closed and

Fig. 2.1: Cross-sectional image of composite oxide ceramics, a low-porosity material[5]

inaccessible pores or open-interconnected, passing or dead end. Furthermore, they differ in their shape which could be cylindrical, conical, spherical or as slits[4] (Fig. 2.1) (Fig. 2.2) (Fig. 2.3). In terms of utility and functionality of such porous materials, they prove to be

Fig. 2.2: Two-dimensional reticulated materials with square pores[6]

considerably advantageous, especially within the architectural world. One of those which has catalysed great attention and interest in further development over the last forty years is porous metals, divided into metals foams, metal sponges

Fig. 2.3: Three-dimensional reticulated foamed materials: nickel foam and iron foam[7]

[3] Ali, S., 8 January 2012. Characterization of Powders, Porous Solids and Suspensions. [online]. Available from: https:// www.slideshare.net/sgarrab/mate-280-characterization-of-powders-and-porous-materials [Accessed 19 April 2018]Paet Joseph Martin. 11 December 2010. Plant tissues and organs. [online]. Available from: http://www.dictionary.com/browse/ porosity [Accessed 18 June 2018] [4] Liu, P. S. and Chen, G. F., (2014) Porous Materials. Processing and Applications, Tokyo: Elsevier Inc. [5] Fig. 2.1 Cross-sectional image of composite oxide ceramics, a low-porosity material. [online]. Available from: https:// www.sciencedirect.com/science/article/pii/B9780124077881000010#s0015 [Accessed 17 June 2018] [6] Fig. 2.2 Two-dimensional reticulated materials with square pores. Ibid [7] Fig. 2.3 Three-dimensional reticulated foamed materials: nickel foam and iron foam. Ibid

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

and Nanoporous metals[8] (Fig. 2.4) (Fig. 2.5) (Fig. 2.6). Their porosity is achieved through different chemical and physical processes[9]. Not only do they possess Fig. 2.4: Representative examples of

metallic foams prepared either by direct (a and b) or by indirect (c and d) foaming techniques [11]

the typical features of metals (ductility, weldability and electrical conductivity) making them fulfil structural and functional purposes, but also they have undergone an

enhancement

other

useful

characteristics. Lightweight, vibration and noise attenuation, low thermal conductivity and sound absorption are some of the Fig. 2.5: Representative examples of metal sponges prepared by different routes [12]

properties which have increased the value and application of this class of metals[10] (Fig. 2.7). Another beneficial architectural material, which engaged us personally, is clay. Its first outstanding feature lies in its

Fig. 2.6: Representative examples of nanoporous metals [13]

capability to work as a porous material in its raw state. In fact, at that stage clay, due to its porosity, is able to absorb water, becoming completely malleable and suitable to be freely modelled. Yet, clay, exposed to a firing process which

Fig. 2.7: Examples of application of porous aluminium [14]

heats the material up to temperatures above the values of dehydration (greater

[8] Kennedy, A., 1 February 2012. Materials thought leaders. [online]. Available from: https://www.azom.com/article. aspx?ArticleID=5940 [Accessed 19 April 2018] [9] Ibid [10] Ibid [11] Fig. 2.4 Representative examples of metallic foams prepared either by direct (a and b) or by indirect (c and d) foaming techniques [online]. Available from: http://pubs.rsc.org/en/Content/ArticleHtml/2015/MH/c4mh00244j [Accessed 18 April 2018] [12] Fig. 2.5 Representative examples of metal sponges prepared by different routes. Ibid [13] Fig. 2.6 Representative examples of nanoporous metals. Ibid [14] Fig. 2.7 Examples of application of porous aluminium. [online]. Available from: https://www.exxentis.com/ anwendungen/ [Accessed 19 April 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

than 1000° C), is subjected to permanent

out to be particularly debatable and

chemical alterations which bond the

controversial. What is porous architecture?

molecules tightly together, bestowing

Is it a conception pursued and applied

hardness and durability to the object and

only to the facades of a building, its

leading the material to lose completely its

external skin which loses materiality

porosity[15]. Due to these characteristics

acquiring transparency and fostering

fired clay is extremely versatile, finding

visual interaction between the inside

large application in all sectors in the

and the outside? Or does it involve the

building industry (Fig. 2.8) (Fig. 2.9).

spatial and functional arrangement of the volumes and the masses constituent in the

2.2 Porosity in architecture When the scale of porosity, as the subject

If we concurred with the latter, it would

of the current argument, becomes

be reasonable to provide as a suitable

the

deriving

example the theoretical and philosophical

interpretations and implications turn

fundaments of the modern architectural

Fig. 2.8: Examples of clay applications:

Fig. 2.9: Examples of usage of ceramics.

architectural

one,

the

bricks, floor tiles and roof tiles [16]

building?

Lydia johnson ceramics[17]

[15] Woodford, C., 7 June 2018. Ceramics. [online]. Available from: https://www.explainthatstuff.com/ceramics.html [Accessed 6 July 2018] [16] Fig. 2.8 Examples of clay applications: bricks, floor tiles and roof tiles [online]. Available from: http://www.ugabox. com/business/directory/clay-products.html [Accessed 6 July 2018] [17] Fig. 2.9 Examples of usage of ceramics. Lydia johnson ceramics [online. Available from: http://e2.turningearth.uk/ lydia-johnson/ [Accessed 6 July 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

movement of De Stijl. Neoplasticism

dimensional elements which, at the same

architects,

Rietveld,

time, divide and interconnect spaces,

conceived architecture as a compound of

often in an adjustable way by using

straight partition walls whose assembly

movable walls[20], is strongly related to

could only occur perpendicularly[18] (Fig.

that definition of porous architecture.

2.10). The disposition of these diaphragms

Consequently, porosity is achieved here

should generate interpenetration between

by playing with the volumes and arranging

the internal and external environment,

the masses so as to create a flowing spatial

through the artificial masses continuing

interconnection.

such

Gerrit

beyond the limits of the interior space

Nevertheless, I strongly believe that,

[19]

(Fig. 2.11). Here the affinity with

in reality, the above questions were

the conception of porous architecture

incorrectly posed and another example

mentioned above is revealed. The idea of

is significant to elucidate the reasons and

decomposing the volume of a building

understand the real essence of porous

through horizontal and vertical two-

architecture.

Fig. 2.10: Example of perpendicularity of

Fig. 2.11: Model of Maison Particulière

plans in the neoplasticism architecture. Theo van Doesburg Contra-Construction Project (Axonometric) 1923 [21]

(Private House), Theo van Doesburg and Cornelis van Eesteren [22]

[18] Wikipedia, 22 April 2018. De Stijl. [online]. Available from: https://it.wikipedia.org/wiki/De_Stijl [Accessed 7 July 2018] [19] Ibid [20] Blogger. 2018. Storia dell’architettura moderna. De Stijl. [online]. Available from: http:// storiadellarchitetturamoderna.blogspot.com/2013/06/de-stijl.html [Accessed 7 July 2018] [21] Fig. 2.10 Example of perpendicularity of plans in the neoplasticism architecture. Theo van Doesburg ContraConstruction Project (Axonometric) 1923 [online] Available from: https://www.moma.org/collection/works/232 [Accessed 7 July 2018] [22] Fig. 2.11 Model of Maison Particulière (Private House), Theo van Doesburg and Cornelis van Eesteren. [online]. Availabe from: https://it.pinterest.com/zlatko928/620-bauhaus-de-stijl-neoplasticism/?lp=true [Accessed 7 July 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

Fig. 2.12: Simmons Hall dormitory, MIT, Steven Holl Architects [26]

The design of Simmons Hall, one of

permeability, to attain a series of favourable

the student residences at MIT, by Steven

effects both at the urban scale, through

Holl, is a symbolic demonstration of how

an improved visibility and accessibility,

the concept of porosity is borrowed by

and at the building scale, with a better

biology and chemistry and transposed in

light penetration and air circulation and

“a tectonic-urban context”[23] (Fig. 2.12).

communication between outside and

The characteristics of pores and porous

inside[25]. The tectonic actualization of

materials were exploited as tectonic

porosity was pursued, in the design

opportunities to originate a porous

process, in various ways and to different

architectural morphology. Holl, in one

degrees of permeability, despite obeying

of his public lectures, proposed: “What if

the common rule to guarantee as much

one aspect of a site – porosity – becomes

interaction as possible between exterior

a concept? Porosity can be a new type

and interior. Large mass-recessions were

of being...”[24]. The concept of porosity

designed as vertical porosity. Horizontally,

was part of a greater hypothesis of

the solution presented large protruding

[23] Kotsopoulos, S. D. 2007. Design Concepts in Architecture: The Porosity Paradigm. International Journal of architectural computing. [online]. 06(03), pp. 337-358. Available from https://www.researchgate.net/ publication/221467193_Design_Concepts_in_Architecture_the_Porosity_Paradigm? [Accessed 10 May 2018] [24] Ibid [25] Ibid [26] Fig. 2.12 Simmons Hall dormitory, MIT, Steven Holl Arhcitects [online]. Available from: http://arkitekt-ur.blogspot. com/2013/11/mit-simmons-hall-by-steven-holl.html [Accessed 6 July 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

masses (Fig. 2.13) (Fig. 2.14). In the overall

were allocated to penetrate the building

picture, a multitude of windows of different

from bottom to top[27] (Fig. 2.17) (Fig. 2.18).

size was distributed on the facades (Fig.

It is evident, in this project, how porosity

2.15) (Fig. 2.16). Finally, freeform cavities

is envisioned in the entirety of the design.

Fig. 2.13: Study for the application of

horizontal and vertical porosity. Simmons Hall, MIT [28]

Fig. 2.15: Sketch for the porosity on

Fig. 2.14: Outcome of the vertical and

horizontal porosity design. Simmons Hall, MIT [29]

Fig. 2.16: Outcome of the porous facade

the facade. Simmons Hall, MIT [30]

through the multitute of windows. Simmons Hall, MIT [31]

Fig. 2.17: Sketch for the vertical

Fig. 2.18: Detail of the vertical porosity

cavities. Simmons Hall, MIT [32]

through the cavities. Simmons Hall, MIT [33]

[27] Kotsopoulos, S. D. 2007. Design Concepts in Architecture: The Porosity Paradigm. International Journal of architectural computing. [online]. 06(03), pp. 337-358. Available from https://www.researchgate.net/ publication/221467193_Design_Concepts_in_Architecture_the_Porosity_Paradigm? [Accessed 10 May 2018] [28] Fig. 2.13 Study for the application of horizontal and vertical porosity. Simmons Hall, MIT [online] Available from: https://www.e-architect.co.uk/boston/simmons-hall-boston [Accessed 12 May 2018] [29] Fig. 2.14 Outcome of the vertical and horizontal porosity design. Simmons Hall, MIT. Ibid [30] Fig. 2.15 Sketch for the porosity on the facade. Simmons Hall, MIT [online]. Available from: http://arkitekt-ur. blogspot.com/2013/11/mit-simmons-hall-by-steven-holl.html [Accessed 12 May 2018] [31] Fig. 2.16 Outcome of the porous facade through the multitute of windows. Simmons Hall, MIT. Ibid [32] Fig. 2.17 Sketch for the vertical cavities. Simmons Hall, MIT. Ibid [33] Fig. 2.18 Detail of the vertical porosity through the cavities. Simmons Hall, MIT. Ibid

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

Neither a piercing process of the skin,

should promote public activities and give

nor creation of a flow of communicating

ground for mobility networks to link them

spaces. The ideal of porosity affects

to other areas of the city, but, at the same

architecture at all its levels. And beyond.

time, nurture the harmonic combination of

2.3 Porosity on an urban scale

private and public[35].

Bearing in mind Steven Holl’s designing

Nevertheless, the necessity of a porous

model, it is natural to acknowledge that

urban fabric is not only craved in those

architectural and urban scales, in regard to

cities characterised by a shortage of

the topic of porosity, are relatively linked.

regulation guiding the actual random

Undoubtedly, porosity in urbanism has

urban growth.

its own connotations. It is an issue which, especially in the last thirty years, has been highly debated, since its multiple implications

the

environmental,

political, economic and social spheres. If we think about the slum communities, in countries such as South-America or India, which host a rapid haphazard growth in

Fig. 2.19: Slum Housing in El Salvador [36]

population with no planned development, leading to a stack of buildings inhabited by squatters, an urgent necessity of porosity is evident[34](Fig. 2.19) (Fig. 2.20). The need of open spaces, with all essential amenities between these stacks, is urgent. They should serve as intermediate spaces with public features, but a private feel: they

Fig. 2.20: Favela housing in Rio de Janeiro. Picture by Paul Stallan [37]

[34] Jimenez, A., 3 June 2016. Visual Porosity and Scale: Architecture Thesis. [online]. Available from: https://issuu.com/ andresjimenez08/docs/thesis-v7-sm [Accessed 7 July 2018] [35] Stratis, S. 2012. Creating a porous urban connective tissue. [online]. Available from: http://admin.brainserver. net/uploads/aau/projects/ARTICLES/ARTICLES_BY_SOCRATES_STRATIS_/WelcomeBackToMyBackYard/ WelcomeBackInMyBackYard.pdf [Accessed 7 July 2017] [36] Fig. 2.19 Slum Housing in El Salvador. [online]. Available from https://www.povertyactionlab.org/evaluation/slumhousing-upgrading-el-salvador-mexico-and-uruguay [Accessed 7 July 2018] [37] Fig. 2.20 Favela housing in Rio de Janeiro. Picture by Paul Stallan [online]. Available from https://www.urbanrealm. com/blogs/index.php/2011/05/23/slum-jpg?blog=12 [Accessed 7 July 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Fig. 2.21: Sponge City, Peter Cook 1974[42]

and existing fabric, affecting positively the enclaves themselves and the territory beyond[39]. Fig. 2.22: Section of the Sponge City project, Peter Cook 1974 [43]

In Europe, the scattered urban voids enclosed

between

infrastructure

However, porosity on an urban scale could assume a different connotation for some others, such as Peter Cook,

who has profoundly engaged with the

transport and city development or situated

debate on landscape and architecture. His

in the outskirts between the agricultural

visionary and unconventional project of

land and the city centre necessitate an

Sponge City (1974) (Fig. 2.21) represents

implementation process of urban porosity.

a clear desire of urban porosity, with a

Those voids, acquire the functionality of

diverse intent[40]. He envisaged many

active voids[38]. They constitute potential

possibilities of buildings as landscape or

enclaves where to position public areas,

“enveloped by natural site coverage”[41]. He

services and flows playing the role of

forecasted cities absorbed by the natural

efficient interfaces between public space

environment (Fig. 2.22). He wrote: “... For

[38] Stratis, S. 2012. Creating a porous urban connective tissue. [online]. Available from: http://admin.brainserver. net/uploads/aau/projects/ARTICLES/ARTICLES_BY_SOCRATES_STRATIS_/WelcomeBackToMyBackYard/ WelcomeBackInMyBackYard.pdf [Accessed 7 July 2017] [39] Ibid [40] Wiley and Sons, J. Ltd. 2007. From Mound to Sponge. How Peter Cook Explores Landscape Buildings. [online]. Available from: https://onlinelibrary.wiley.com/doi/pdf/10.1002/ad.419 [Accessed 18 April 2018] [41] Ibid [42] Fig. 2.21 Sponge City, Peter Cook 1974. Wiley and Sons, J. Ltd. 2007. From Mound to Sponge. How Peter Cook Explores Landscape Buildings. [online]. Available from: https://onlinelibrary.wiley.com/doi/pdf/10.1002/ad.419 [Accessed 18 April 2018] [43] Fig. 2.22 Section of the Sponge City project, Peter Cook 1974. Ibid

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

me it becomes even more intriguing if we

material par excellence, through the

pull the vegetal towards the artificial and

middle one with the architectural proposal

the fertile towards the urban but in the end

of a porous wall (Fig. 2.23), to the largest

... to find the magic of a place discovered,

with the environmental, political and social

now thatâ&#x20AC;&#x2122;s architectureâ&#x20AC;?[44]. Thus, Peter

implications of our final proposal: the

Cook encouraged the idea of joining

porous skyscraper (Fig. 2.25). In addition,

together architecture and landscape

we further divided the middle scale into

in a united environment, suggesting a

multiple sub-levels as a result of the cross-

different conception of urban porosity, as

scale design development (Fig. 2.24). We

interpenetration between the natural and

designed and combined graded sizes

the artificial environment.

of our components, in order to enhance the aesthetic quality, fulfil functional

2.4 Scalability of our architectural proposal

necessities and optimise the different scale

After such an extensive discourse on

applications.

the different scales of porosity, a proper

Scalability has always been a key-word

conclusion should focus on understanding

of our design research. We pursued it in

which

multiple ways and with different strategies.

ones

our

design

research

encompasses.

Starting from the basic component, we

In reality, all of them. From the smallest

developed the language by designing

scale, by using the porous building

proportionally smaller components (a

Fig. 2.23: Porous wall. Architectural scale.

Fig. 2.24: Cross-scale design development

[44]â&#x20AC;&#x192;Wiley and Sons, J. Ltd. 2007. From Mound to Sponge. How Peter Cook Explores Landscape Buildings. [online]. Available from: https://onlinelibrary.wiley.com/doi/pdf/10.1002/ad.419 [Accessed 18 April 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

quarter of the basic size), to be used for

proposal.

the blueprint of furniture, and bigger ones

Finally, scalability was relevant to the

(four times the basic size), to allow their

acknowledgment that we needed to draw

realistic usage as a screen in the skyscraper

upon two different fabrication techniques,

Fig. 2.25: The porous skyscraper 20

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

based on two distinctive architectural

scale, such as a pavilion, they can guarantee

applications. In fact, at a larger scale - the

structural stability, demanding their full

skyscraper -, our ceramic geometry can

solidity, though. They are able to behave as

only perform non-structural functions,

a self-supported brick wall, providing the

such as a shading system, hence requiring

benefits of a porous screen and dazzling

the components to be lighter, hollow

with their unique and harmonic aesthetic

internally and supported by an integrated

design (Fig. 2.27).

structure (Fig. 2.26). Instead, on a minor

Fig. 2.26: The metal frame as a support of the light clay shading system

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Fig. 2.27: Application of the structural solid components as a pavilion.

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

DIFFERENT LAYERS OF POROSITY

The topic of layers of porosity has

dynamic porosity language, occurring on

profoundly pervaded our project since

diverse levels and with distinctive features,

the very beginning of the study. The idea

displaying continuing transformations,

of using porous discrete components to

apparently random variations and illogical

design a continuously porous architectural

modifications, capable of captivating

mass, within which to conceive a variable

the observer in an exceptionally active

porosity in the overall shape, itself

experience. Nonetheless, it was meant to

manifests the existence of different layers

be a conscious dynamism, an apparently

of porosity. A first layer is inside each

random design always controlled and

modular component. A second layer is

managed by the logicality of mathematical

in the whole design of the architectural

formulas of parametric software.

proposal.

Going back to the two layers previously

Two levels of porosity: two different

described, it would be probably interesting

generating rules and two different

and meaningful (for a more appropriate

purposes, but working together for the

understanding of their characteristics)

same purpose. Which was: creating a

to introduce a parallelism with what, in 24

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

nature, a porous layered structure implies. A valid example which represents how multiple layers of material, in the same body, with various grades of porosity, contribute to the perfect execution of any activity, despite performing different functions is that of plant leaves. Should we want to analyse a leaf tissue structure, through a Scanning electron micrograph (SEM) it would be easy to recognise its subdivision in three different parts (Fig. 3.1) The external layer of cells is the epidermis[45]. This represents a nearly non-porous layer, as the epidermis is covered entirely, on its outer part, by a thin waterproof skin, the waxy cuticle, which prevents the loss of water and moisture. However, it holds a series of pores, called stomata, which are small openings controlling the inward and outward transition of gases (carbon dioxide, oxygen and water vapour)[46]. Below the epidermis

Fig. 3.1: Coloured scanning electron micrograph (SEM) of a leaf tissue structure[47]

is the palisade mesophyll, a low-porosity layer made of long column-like cells tightly packed together which, containing a large number of chloroplasts, permits the photosynthesis process by absorbing

[45] Gschmeissner Steve . 30 April 2013. Leaf Tissue Structure, Sem. [online]. Available from: https://fineartamerica.com/ featured/leaf-tissue-structure-sem-steve-gschmeissner.html [Accessed 18 June 2018] [46] Ibid [47] Fig. 3.1 Coloured scanning electron micrograph (SEM) of a leaf tissue structure. [online]. Available from: https:// fineartamwww/featured/leaf-tissue-structure-sem-steve-gschmeissner.html [Accessed 18 June 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

energy from sunlight[48]. The central part of

porosity which complement each other,

the leaf is the spongy mesophyll, formed

displaying not only an appealing but

of high-porosity layers with an open-pore

also perfectly integrated and operational

structure. These large interconnected

architectural chunk.

spaces between the cells allow the storage and exchange of gases, essential to the

3.1 The first layer

photosynthesis [49] (Fig. 3.2).

The first layer of porosity, as already

Likewise the three layers of the leaf, although

characterised

mentioned, is obtained in each module.

various

Primarily, the reason why we pursued

grades of porosity and different roles,

such a porous modular component was

work perfectly together to execute the

to guarantee an overall diffused porosity.

vital functions of the plant, our proposal

The idea was to create a continuously

is conceived of two layers of different

hollow architectural object, capable of

CUTICLE EPIDERMIS PALISADE MESOPHYLL SPONGY MESOPHYLL

Fig. 3.2: Different layers of a leaf tissue structure[50]

[48] Paet Joseph Martin. 11 December 2010. Plant tissues and organs. [online]. Available from: http://www.dictionary. com/browse/porosity [Accessed 18 June 2018] [49] Ibid [50] Fig. 3.2 Different layers of a leaf tissue structure. [online]. Available from: https: https://www.slideshare.net/j0martin/ plant-tissues-and-organs [Accessed 18 June 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

exploiting the multiple advantages of a

module. This will appear evident when

porous structure. Porous architecture,

illustrating the last stage of this specific

more exactly porous walls, represent the

design process.

wisest natural system to accomplish an

The first proposal of modular clay

ideal indoor microclimate and illumination

components derived from the awareness

(Fig. 3.3) and (Fig. 3.4). By manipulating the

of the geometric limits of the traditional

weave of porosity, it is possible to cool the

clay bricks. We wanted to attribute three-

temperature diversely and determine the

dimensions and enhance the aesthetic

amount of sunlight penetrating inside.

value of our basic geometry. For this

“Primarily” is used at the beginning of the

reason, inspired by the Rubik’s Cube

previous paragraph as it is undeniable that

puzzle, we explored the possibility to

it was an aesthetic factor in the reasoning

construct discrete components resulting

which led us to design such a porous clay

from the aggregation of multiple voxel

Fig. 3.3: Example of shadow in architectural patio[51]

Fig. 3.4: Effect of sunlight passing through a

porous wall. San Telmo Museum, San Sebastian, Nieto Sobejano Arquitectos[52]

[51] Fig. 3.3 Example of shadow in architectural patio. [online]. Available from: https://www.loverush.com.au/la-bellevie/ [Accessed 18 June 2018] [52] Fig. 3.4 Effect of sunlight passing through a porous wall. San Telmo Museum, San Sebastian, Nieto Sobejano Arquitectos. [online]. Available from: https://www.archdaily.com/208764/san-telmo-museum-nieto-sobejano-arquitectos [Accessed 18 June 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Fig. 3.5: Possibilities of components depending on the number of cubes aggregated

cubes (Fig. 3.5).

cube-module, was not effective at creating

Subsequently, when moving from basic

and controlling porosity. In order to be

discrete components - whose assembly

more efficient, we had to envision porosity

insured a certain level of porosity in the

within the module itself. For this reason,

overall design but without any rational

we dismissed the closed-cell-like polycube,

control - to a cubic modular component

the Soma Cube, and oriented our research

(Soma Cube), we faced the need of a new

towards a particular type of polycube

strategy. The logic of Soma Cube (Fig.

called Baiocchi figure, applied to Beszel

3.6), which entailed the use of a limited

Polycube. â&#x20AC;&#x153;A Baiocchi figure is a figure

number of the basic components and only

formed by joining copies of a polyform

in particular combinations so as to form a

and having the maximal symmetry for the

Fig. 3.6: One example of the solutions of Soma cube[53] [53]â&#x20AC;&#x192;Fig. 3.6 One example of the solutions of Soma cube. [online]. Available from: https://en.wikipedia.org/wiki/Soma_ cube [Accessed 18 June 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

TRICUBES

TETRACUBES

PENTACUBES

HEXACUBES

Fig. 3.7: Examples of monocube, dicubes, tricubes, tetracubes, pentacubes and hexacubes for Baiocchi Figures.[54]

[54]â&#x20AC;&#x192;Fig. 3.7 Examples of monocube, dicubes, tricubes, tetracubes, pentacubes and hexacubes for Baiocchi Figures. [online]. Available from: http://www.recmath.org/PolyCur/besbaiocchi/index.html [Accessed 14 February 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

polyform’s class. For polycubes, that means

inside but also along the edges and in

cubic symmetry”[55] and “a Besźel Polycube

the corners, since it was the only way to

is a polycube whose cells all have at least

achieve a clearly detectable and variable

two even coordinates.”[56] According to the

porosity in the aggregation of a multitude

definitions of these specific geometries, we

of modules. Having attained a reasonably

studied and developed the Baiocchi figures

satisfying result, we proceeded to apply

applied to Beszel Polycubes of orders 1 to 5

these modular geometries to different

(Monocube, Dicubes, Tricubes, Tetracubes,

languages of assembly, by testing and

Pentacubes, Hexacubes) (Fig. 3.7) so as to

comparing the outcomes of multiple

generate different modular components

scripts based on variable mathematical

and test various porosities. Not only did

assumptions (Fig. 3.8).

we try to void the cubic module from

At this point, we decided to implement

Fig. 3.8: Outcome of the combination of the first solutions of porous modules. [55] Sicherman George. 12 September 2017. Baiocchi Figures for Besźel Polycubes. [online]. Available from: http://www. recmath.org/PolyCur/besbaiocchi/index.html [Accessed 14 February 2018] [56] Ibid

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

the last step in the design of the first layer

marching cube logic, obtaining 256

of porosity. Particularly in this investigation

different configurations of the cube,

of a new porosity language, the aesthetical

since the 28 possible combinations of the

purpose/intent became evident.

curved corners[57] (Fig. 3.9). Subsequently,

We were looking for more complexity.

we applied the same marching cube

We wanted to explore more intricate

subtractive process to the porous polycubes

geometries. At first, we foresaw an

by removing the corner components

opportunity to create more geometric

correspondent to the hollowed rounded

dynamism by intersecting the straight

corners of the modular cubes (Fig. 3.10) (Fig.

cubic module with its antipodal geometry,

3.11). However, despite the marching cube

a sphere. The resulting volume consisted

algorithm rationalizing the displacement

of a cube with a concave rounded corner.

of the more articulate modules, according

We employed this rule following the

to a predesigned pattern, the overall

Fig. 3.9: Some of 256 configurations of the cubic module, obtained by

intersecting the cube with a sphere, following the marching cube logic.

[57]â&#x20AC;&#x192;Bourke, P., May 1994. Polygonising a scalar field. [online]. Available from: http://paulbourke.net/geometry/ polygonise/ [Accessed 9 March 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Fig. 3.10: Application of the marching cube subtracting process to the polycubes.

COMPONENTS

ROTATE & COMBINE

POROSITY

COMPONENTS

ROTATE & COMBINE

POROSITY

－

Fig. 3.11: Application of the marching cube subtracting process to the polycubes.

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

configuration proved to be ineffective, particularly in terms of structural stability. For this reason, we changed strategy. Based

interesting

and

suitable

references – Frank Lloyd Wright, Ennis House and La Miniatura (Fig. 3.12) (Fig. 3.13) – we started drawing linear patterns travelling throughout the porous polycube module, from outside to in. The lines of the pattern represented the further emptiness

Fig. 3.12: Ennis House, Frank Lloyd Wright, Los Angeles, California[58]

to be built in the module, guidelines identifying the extra matter to be removed (Fig. 3.14). Drawing more and more lines, we were increasingly gutting and almost dematerialising the module. The goal was to generate articulate transparency by subtraction of matter which follows a carefully designed motive of lines. By doing this and after combining different outcomes (Fig. 3.15) we decided to take

Fig. 3.13: La Miniatura, Frank Lloyd Wright, Los Angeles, California[59]

this language to the extreme. Thus, the pattern, from guidelines for emptying the matter became the matter itself. The motive of lines defined the solid; all the rest within the module was excess, insignificant and so it was eliminated in order to generate

Fig. 3.14: Some examples of the module cut following the pattern of lines.

[58] Fig. 3.12 Ennis House, Frank Lloyd Wright, Los Angeles, California. [online]. Available from: https://whiteriver.com/ products/cube-paperweight-ennis-design-2-5-sq [Accessed 9 May 2018] [59] Fig. 3.13 La Miniatura, Frank Lloyd Wright, Los Angeles, California. [online]. Available from: http://www.sytyson.com/ storer-house-par-frank-lloyd-wright/ [Accessed 9 May 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Fig. 3.15: Two examples of combination of different modules cut according to the pattern of lines.

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

transparency and porosity. Hence, a new, totally revolutionised geometry. The final geometry. The final design of the first layer of porosity (Fig. 3.16) (Fig. 3.17).

BASIC MODULE

NEW PATTERN

BASIC MODULE WITH PATTERN

INCREASE OF POROSITY BY CUTTING MORE

Fig. 3.16: Final geometry

INSTABILITY OF COMPONENTS

ADD SUPPORTING COMPONENTS

THE PATTERN BECOMES THE GEOMETRY

OPTIMIZE THE STABILITY BY INCREASING THE TOUCHING SURFACES

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Fig. 3.17: Final geometry in the overal design

3.2 The second layer

architectural chunk. More exactly, a wall.

The second layer of porosity, as specified

Therefore, it regards the displacement

before, concerns the overall configuration

of voids throughout the wall, their

of our architectural proposal. It involves a

dimensions and forms.

bigger scale, represented by the assembly

At this stage, the designing process of

of the porous modules to generate our

the second level of porosity will not be 36

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

detailed, since it will be argued attentively and exhaustively in Chapter 5 of this report. However, all the premises which have led us to qualify this level with its own functions, scope and aesthetical peculiarities will be delineated, premises Cool air Warm air

which have also suggested resorting to different design strategies. A porous wall is beneficial for its capability to provide mild ventilation, naturally screen the indoor environment from solar radiation and, thus, reduce the temperature (Fig.

COOLING Light

3.18). Additionally, it would be a valid system to guarantee a certain grade of privacy and veil those inside from external sight, despite preserving the advantages of natural aeration. Yet, our porous wall is even more advantageous. It, solely, offers the opportunity to change and adjust itself depending on the specific requirements, thanks to the parametric

SUNLIGHT Fig. 3.18: The benefits of a porous wall

control of its design. By implementing different data entry in the script, in the form of algorithms or other mathematical formulas, we are able to decide frequency,

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

dimension and shape of the voids (Fig.

seasons, climate, location, height of the

3.19). We can distinguish high-porosity

floor and so on. Therefore, we can depict

areas from low-porosity ones and big-size

it as flexible porosity, which changes

pores from small ones, influenced by the

configuration and appearance depending

mutation of factors such as sun exposure,

on functional needs, but always maintains

Fig. 3.19: Variation of the second layer of porosity through the parametric control of its design

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

the beauty and the attractive aesthetic of a

between the porosity design of the module

harmonic combination of 3d modular clay

and its configuration throughout the wall.

components. Also, this balanced image is not only noticeable in the overall design of

3.3 Uniqueness of our design proposal

the second layer of porosity, but it is also

It could be countered that this kind of

intrinsic in the interaction between the

screen wall is already common in countries

large and the small scale, the whole porosity

which typically suffer from hot weather. For

and the single porous module, the second

instance, the traditional Islamic shading

and the first level. The osmosis thoughtfully

system called Mashrabiya performs all

designed and established between the

the services mentioned above (Fig. 3.21).

two layers of porosity represents the core

It has been used since the Middle Age

of the aesthetic fascination and attraction

and accurately designed to fulfil different

of our architectural proposal.

purposes: privacy, protection from the

Marine sponges are able to express such

summer sun, cool airflows, shelter from

an organic perfection of beauty thanks to

sun and rain for people in the street and

their graded porous microstructure[60](Fig.

correction of the footprint form of the

3.20). Likewise, the attractive beauty of

land[61]. Nevertheless, contrary to the

our design could not be achieved without

two-dimensional wooden lattice of the

the perfect equilibrium and integration

Arabic screen, our porous wall fulfils the

Fig. 3.20: Example of marine sponges: Phylum Porifera[62]

[60] Slideshare, 15 March 2009. Poriferappt. [online]. Available from: https://www.slideshare.net/guest0e117cf/ poriferappt [Accessed 9 July 2018] [61] Wikipedia, 11 June 2018. Mashrabiya, [online]. Available from: https://en.wikipedia.org/wiki/Mashrabiya#Utilisation [Accessed 14 May 2018] [62] Fig. 3.20 Example of marine sponges. [online]. Available from: https://thephylumporiferaproject.wikispaces.com/ Callyspongia+plicifera [Accessed 8 July 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Fig. 3.21: Examples of Mashrabiya serving as ventilation and protection for buildings[63]

[63]â&#x20AC;&#x192;Fig. 3.21 Examples of Mashrabiya serving as ventilation and protection for buildings. [online]. Available from: https://www.hommeg.com/moucharabieh-all-on-the-art-and-deco-piece-very-trendy [Accessed 4 July 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

Fig. 3.24: King Fahad National Library, Saudi Arabia, Gerber Architekten[66]

Fig. 3.22: Al Bahar Towers,

Abu Dhabi, Aedas Architects[64]

Fig. 3.23: Larchmont Lotus Building, Los Angeles, XP& Architecture[65]

Fig. 3.25: Casa Walther Moreira Salles, Rio de Janeiro, Olavo Redig de Campos[67]

same functions being qualified by a three-

Architecture (Fig. 3.24); Casa Walther

dimensional structural body, though.

Moreira Salles in Rio de Janeiro, by Olavo

It could also be opposed that, in reality,

Redig de Campos (Fig. 3.25); and so forth.

three-dimensional shading screens are,

However, they all delineate a display of

nowadays, widely used. This is true. A

modern shading facades where porosity

plethora of examples could be pointed

out: Al Bahar Towers in Abu Dhabi, by

hybrid systems – a combination of soft

Aedas Architects (Fig. 3.22); King Fahad

material such as fabric and supporting

National Library in Riyadh Saudi Arabia, by

metal substructure – by organically-

Gerber Architekten (Fig. 3.23); Larchmont

shaped discrete metal components or by

Lotus Building in Los Angeles, by XP&

geometrically convoluted but repetitive

attained

either

sophisticated

[64] Fig. 3.22 Al Bahar Towers, Abu Dhabi, Aedas Architects. [online]. Available from: m/270592/al-bahar-towersresponsive-facade-aedascom/moucharabieh-all-on-the-art-and-deco-piece-very-trendy [Accessed 4 July 2018] [65] Fig. 3.23 Larchmont Lotus Building, Los Angeles, XP& Architecture. [online]. Available from: https://archinect. com/firms/project/17201981/larchmond-lotus-xp-architecture-designs-a-climate-regulating-self-cleaning-and-imageimproving-new-envelope-for-the-larchmont-medical-center-in-los-angeles/17201983 [Accessed 4 July 2018] [66] Fig. 3.24 King Fahad National Library, Saudi Arabia, Gerber Architekten. [online]. Available from: https://it.pinterest. com/pin/489766528198435415/?lp=true [Accessed 4 July 2018] [67] Fig. 3.25 Casa Walther Moreira Salles, Rio de Janeiro, Olavo Redig de Campos. [online]. Available from: https:// belblasiarquitetura.wordpress.com/tag/arquitetura/ [Accessed 4 July 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

concrete modules. They are unable to amaze with the depth of a threedimensional structure, ensure solar control and light transmission performances and, at the same time, provide the advantageous benefits which only clay can offer. Clay is worldwide, cheap, easily accessible, natural, strong, highly fireproof, and absolutely sustainable, not only as the material itself but also in its manufacturing procedures. Even though there are examples of clay screen usage, for instance the Termitary House in Thanh KhĂŞ District, Vietnam, by Tropical Space (Fig. 3.26), they are the result of a different and creative assembly of traditional brick masonry, which simply increases the distance between the bricks to generate voids. Hence, the exceptionality and innovation of our proposal undeniably emerges. It assures internal thermal and visual comfort, minimizing costs and energy consumption due to the intrinsic properties of clay, and never sacrifices the geometrical exploration and design creativity underpinning the pursuit of seductive aesthetic quality.

Fig. 3.26: Termitary House, Thanh Khe District, Vietnam, Tropical Space[68]

[68]â&#x20AC;&#x192;Fig. 3.26 Termitary House, Thanh Khe District, Vietnam, Tropical Space. [online]. Available from: https://www. archdaily.com/594339/termitary-house-tropical-space [Accessed 4 July 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

POROSITY IN A DUALISM OF SPACE AND MATTER

The definition of the word porosity, as

infinite, yes and no, outside and inside,

found in most dictionaries and scientific

being and non-being, and so on. Would,

books, contains a highly-problematic

then, our idea of porosity be ascribable in

controversy: “the ratio, expressed as a

such a philosophical speculation, evoking

percentage, of the volume of the pores

the same bipolarity between emptiness

or interstices of a substance, as a rock or

and substance? Besides, does the dialectic

rock stratum, to the total volume of the

of emptiness and fullness correspond

mass”[69]. As the ratio of the volume of

to the antithesis of space and matter? Is

the space to the volume of the mass, the

it reasonable to identify the ontological

concept of porosity suggests a comparison

conception of space with the idea of

between the void, the interstices between

absence and void, and the expression

the particles of material, and the solid,

of matter with the substance filling that

its mass. Duality of void and fullness has

emptiness?

always been one of the most debated

In order to elucidate and respond to the

arguments in architecture, very often

raised questions, in the first place I would

related to the dialectics of finite and

make reference to the notion of emptiness

[69] Houghton Mifflin Harcourt Publishing Company. 2011. Etymology and definition of the word porosity. [online]. Available from: http://www.dictionary.com/browse/porosity [Accessed 26 April 2018].

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

conceived by Taoism and the Chinese

it limits, as it is not a subsisting being

cosmology. In the beginning, the original

itself but it is the condition determining

essence of the cosmos was tàixū (太虛),

being. Hence, space and matter are in

the Great Emptiness, also called wújìn (

a relation of mutual implication[74]. Yet,

无尽), the Endless[70]. This non-existence

what is more interesting, and radically

originated universe and life in it. In all

significant

Chinese culture, the emptiness is, then, the

communication of our design proposal, is

essential condition for the manifestation

the differentiation delineated by Aristotle

and transformation of being[71]. Not only

between space and form, as both limits of

is this true in physics and medicine, but

the being[75]. In primis, limit is what makes

also in the Chinese arts. For instance, in

the appearance and the discernment

painting, it is often the unpainted parts

(διαίρεσις) of being possible.

that prevail over the painted ones, as if

However, διαίρεσις is not

to say it is the emptiness to determine

sufficient for being to be, since its substance

the fullness[72]. Therefore, in the Chinese

is due to είδος, form, which is a

culture the void as non-existence is the

necessary condition. Form and space are

root and the cause of being.

both limits (πέρατα): form is the limit

for

the

cognizance

and

Although denying the existence of

of the being (πράγμα), space is the

emptiness, since it would make the

limit of the entity embracing the being

movement of bodies impossible, Aristotle,

(σώμα)[76]. Therefore, we can conclude

in book IV of Physics[73], conceives space in

that if the limit of a body is its shape, space,

the same causal role as Taoism interprets

as also a limit, is the shape of the being

the void. Space is what contains all things.

which embraces that body. Essentially, it is

It is limit and determiner of each thing.

the shape of the void embracing the body.

However, contrary to the essentiality and

Such a definition suggests that space

unavoidability of the Great Emptiness,

constitutes the tangible and perceivable

space cannot exist without the body which

distinction of bodies. Through space the

[70] Sotte, L., Minelli, E., Giovanardi, C. M., Matrà, A., and Schiantarelli, C., (2006), Fondamenti di Agopuntura e Medicina Cinese, Milano: CEA. [71] Ibid [72] Ibid [73] Ackrill, J. L., and Judson, L., (1993), Aristotle Physics: books III and IV, Oxford: Clarendon Press. [74] Ibid [75] Ibid [76] Ibid

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Fig. 4.1: Untitled (One Hundred Spaces) 1995 by Rachel Whiteread[78]

Fig. 4.2: Untitled (Book Corridors) 1998 by Rachel Whiteread[79]

being is determined in its unique, actual and

artworks, space does not only represent

concrete presence. Consequently, could

the medium to shape and give consistency

we assert that the Aristotelian theories

to objects. The concept of qualitative

represent the philosophic fundament

experience of space is here emphasised to

of the qualitative experience of space?

its extreme, almost obsessive, expression.

Could we actually believe in a qualitative

Space becomes an object itself, acquiring

characterisation and differentiation of

those characteristics of aesthetic, visibility

space? Would it be realistic to debate the

and materiality typical of matter (Fig. 4.1).

aesthetic, visual and tangible features of

Rachel Whiteread “makes the invisible

space?

visible”[77], by casting the negative space,

Undoubtedly, it would be if we looked at Rachel Whiteread’s work. In her cast

the space in-between and around things (Fig. 4.2).

[77] Whiteread Rachel. 2017. Exhibition at Tate Britain [online]. Available from: http://www.tate.org.uk/art/artists/rachelwhiteread-2319/five-things-know-rachel-whiteread [Accessed 24 May 2018] [78] Fig. 4.1 Untitled (One Hundred Spaces) 1995 by Rachel Whiteread. [online]. Available from: http://www.artzip.org/ rachel-whiteread [Accessed 24 May 2018] [79] Fig. 4.2 Untitled (Book Corridors) 1998 by Rachel Whiteread. [online]. Available from: http://www.tate.org.uk/art/ artists/rachel-whiteread-2319/five-things-know-rachel-whiteread [Accessed 24 May 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

What we see and perceive is no longer

(Fig. 4.3), with the stairs leading nowhere,

the objects occupying the space but,

evokes, almost with the same restlessness,

instead, the space occupied and shaped

the oneiric vision of Escher (Fig. 4.4) and

by the objects. “It’s the invisible spaces

Piranesi (Fig. 4.5) of impossible objects,

around us that Whiteread has turned our

allegorising the illusion of trapped and

focus to.”[80]It is the modelled space to

unattainable dreams. The glass cast of

inspire emotions and address stories[81].

a doll’s house fulfils a childhood fantasy,

The white plaster Untitled (Stairs), (2001)

allowing the viewers to release their

Fig. 4.3: Untitled (Stairs), 2001 by Rachel

Fig. 4.4: Relativity, 1953, by Maurits Cornelis

Fig. 4.5: The Prisons, 1750, Giovanni Battista

Fig. 4.6: Ghost II, 2009 by Rachel

Whiteread.[82]

Piranesi[84]

imagination thanks to a journey of the

Escher[83]

Whiteread[85]

If we wanted to relate the artistic

sight which moves along the corridors

abstraction of the vision of Rachel

and penetrates through the walls into

Whiteread to our architectural proposal

chambers, despite the doors being closed

the following question would arise

(Fig. 4.6).

naturally: is the porosity of our wall meant

[80] Whiteread Rachel. 2017. Exhibition at Tate Britain [online]. Available from: http://www.tate.org.uk/art/artists/rachelwhiteread-2319/five-things-know-rachel-whiteread [Accessed 24 May 2018] [81] Ibid [82] Fig. 4.3 Untitled (Stairs), 2001 by Rachel Whiteread. [online]. Available from: http://www.tate.org.uk/art/artists/ rachel-whiteread-2319/five-things-know-rachel-whiteread [Accessed 24 May 2018] [83] Fig. 4.4 Relativity, 1953, by Maurits Cornelis Escher. [online]. Available at: http://artattack911.com/mc-escher-mindbending-art-bay-area-and-peninsula-art-classes-for-all-ages/ [Accessed 24 May 2018] [84] Fig. 4.5 The Prisons, 1750, Giovanni Battista Piranesi. [online]. Available at: https://en.wikipedia.org/wiki/Giovanni_ Battista_Piranesi#The_Prisons_(Carceri) [Accessed 24 May 2018] [85] Fig. 4.6 Ghost II, 2009 by Rachel Whiteread. [online]. Available from: http://www.artzip.org/rachel-whiteread [Accessed 24 May 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

to be considered as material substance

Leibniz, and Locke, that a new direction

pierced with voids of different size or

in the investigation into the notion of

utter pure space determined and shaped

space started taking shape, giving more

by geometrical extension of matter?

prominence to the subjective sphere[88].

According to the new theories of space of

However, only George Berkeley radicalised

Albert Einstein, the latter seems to be the

the new way of thinking, asserting that the

most appropriate standpoint. In his General

perception of space is impossible without

theory of relativity (1915), he developed a

a series of visual and tactile impressions,

new theory of the physical space based on

such as colours and figures, which are

the notion of “spacetime”[86], namely an

totally subjective[89]. These impressions

“elastic space” which, like an elastic fabric,

abstract from the mind to create an idea

transforms depending on the variation of

of space which, not necessarily, reflects

the presence of matter in it[87].

the external reality. It is an interiorised

Even though Einstein’s theory of the elastic space pertains more to cosmological

and personalised idea and perception of space[90].

and physical studies, it reveals itself

This means that, regardless of any

extremely meaningful and persuasive

acceptable ontological definition and

for the architectural comprehension and

conception of space, there is always a

expression of space. It is a vision exquisitely

sensorial and subjective component which,

poetic, yet very actual, conceiving space

depending on the individual background,

as a malleable reality, which changes its

experiences, temporary disposition and

manifestation and perception according

forma mentis of the observer, will affect

to the presence and changing of any

the perception of space differently, the

substance in it.

substance in it and their interaction.

These considerations seem to suggest

This radical and modern viewpoint creates

a rather gnoseological and psychological

a link between a purely philosophical and

interpretation of space. It was with

a more aptly architectural understanding

[86] Gron, O., Hervik, S., (2007) Einstein’s General theory of Relativity, New York: Springer. [87] Ibid [88] Treccani. 2009. Spazio, dizionario di filosofia. [online]. Available from: http://www.treccani.it/enciclopedia/ spazio_%28Dizionario-di-filosofia%29/ [Accessed 17 May 2018] [89] Ibid [90] Ibid

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

of space. It helps reconnect such a

is caused by a general inability of thinking

philosophical and ontological speculation

and understanding architecture in terms

on it with our design research.

of space. Such an ineptitude concerning

In fact, the void is the primordial

space probably derives from the means

archetype of architecture. It is the essence

of representation of architecture itself:

of architecture, the basis from which

plans, sections and elevations are, for

it is originated[91]. It is space inside the

architects, the instruments to represent

architectural composition of volumes; it is

the architectural volume of buildings.[95]

path and itinerary inside it; it is core in the

And it is undeniable that our judgement of

architecture of the shell.

a building which we have not experienced

Bruno Zevi in his book Architecture

by the more or less appealing aspect of

architecture”.[92]

those representations. However, even

“Architecture, however, does not consist

though a plan or a façade may seem

in the sum of the width, length and height

well-proportioned

of the structural elements which enclose

paper, the building might prove to be

space, but in the void itself, the enclosed

mediocre architecture since the space in

space in which man lives and moves.”[93]

it turns out to be petty and unpleasant.[96]

And again, “The façade and walls of

According to Zevi, beautiful architecture

a house, church or palace, no matter

is “architecture in which the interior space

how beautiful they may be, are only the

attract us, elevates us and dominates us

container, the box formed by the walls;

spiritually”.[97] Beautiful architecture is

the content is the internal space.”[94] Zevi

architecture that not only dazzles with the

complains of the lack of a correct history

attractiveness of its volumes, geometries

of architecture due to an incoherent

and materials but also captivates us with

approach which historians have used to

the perception of the space shaped by

study and analyse buildings. This failure

those volumes. The equilibrium generated

“the

space

(1957)

protagonist

defines of

space

personally is unconsciously conditioned

and

attractive

[91] Scarpato, L., (2010/2011). Nulla è vuoto. Costruire intorno al vuoto: un’analisi critica dell’archetipo primordiale dell’architettura. Unpublished Master’s degree thesis, Politecnico di Milano. [92] Zevi, B., (1957) Architecture as space, New York: Horizon Press. [93] Ibid [94] Ibid [95] Ibid [96] Ibid [97] Ibid

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

by the perfect relation between matter and

a juxtaposition of closed parts. It endorses

space, which together, encompasses man

the opposite idea: modelling voids,

in a four-dimensional experience which

according to a principle of subtracting

is distinctive and unique to architecture.

matter.[98] They recognise in the negative

Architecture needs to be gone through,

space, what follows from the compound

perceived and lived. For this reason,

of the masses, the substantial aim and

we need to learn how to grasp space in

the intrinsic meaning of the designing

architecture and understand it, because

process. In their Alenquer House (2002),

this understanding is the crucial element

Portugal, the core of the project lies on a

to produce a valid and truthful criticism of

labyrinthine continuum of voids unfolding

architecture.

between the prior perimeter wall and the

Among the contemporary architectural

new internal residential nucleus[99] (Fig.

practices, Aires Mateus’ works seem to

4.7). Furthermore, the astonishing spatial

materialise the guidance expressed by

emotion emanating from the paths and the

Zevi the most and transpose the artistic

lines of sight through slender diaphragms

representations of Whiteread to the

and openings turning towards the outside

architectural field. Their designing process

(Fig. 4.8) is revealed in its authentic

declines the conception of architecture as

essence by the reflection and diffusion of

Fig. 4.7: Alenquer House, Portugal, Aires

Fig. 4.8: Alenquer House, Portugal, Aires

Mateus. View of the openings toward the outside[100]

Mateus. Plan and an internal perspective view[101]

[98] Mandolesi, D. 2015. Architetture di Aires Mateus. Tra tensione poetica e rigore formale. Rassegna di architettura e urbanistica, Anno L(147), pp. 93-97 [99] Ibid [100] Fig. 4.7 Alenquer House, Portugal, Aires Mateus. View of the openings toward the outside. [online]. Available from: http://arquitecturadesignetc.blogspot.com/2011/10/manuel-e-francisco-aires-mateus-casa-em.html [Accessed 5 July 2018] [101] Fig. 4.8 Alenquer House, Portugal, Aires Mateus. Plan and an internal perspective view. [online]. Available from: http://twobo.blogspot.com/2010/ [Accessed 5 July 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

the light on the pure white surfaces.[102]

from some mysterious opening to tell us

(Fig. 4.9) It is a new idea of architecture:

how dark it really is. Each space must be

no longer “the learned game, correct and

defined by its structure and the character

magnificent, of forms assembled in the

of its natural light.”[106] Therefore, Kahn

light”[103] as envisioned by Le Corbusier,

virtually identifies the two entities of

but the meditated creation of spaces and

space and light. Light reveals and defines

their relations, unveiled by the light, as

space; it enters into a space through non-

proclaimed by Louis Kahn[104]. He stated

matter that is the void present in the

that space, in architecture, does not exist

solid walls enclosing that space. Thus, the

without natural light[105]. “A plan of a

surrounding wall is the creator of space:

building should be read like a harmony

it, with its openings, lets light through

of spaces in light. Even a space intended

determining space[107].

to be dark should have just enough light

This vision is extremely purposeful to

Fig. 4.9: Alenquer House, Portugal, Aires Mateus. View of the diffusion of light on the white volumes[108]

[102] Mandolesi, D. 2015. Architetture di Aires Mateus. Tra tensione poetica e rigore formale. Rassegna di architettura e urbanistica, Anno L(147), pp. 93-97 [103] Etchells, F., (1970) Towards a new architecture, London: The Architectural Press. [104] Norberg-Schulz, C., (1981) Louis I. Kahn: idea e imagen, Madrid: Xarait Ediciones. [105] Ibid [106] Ibid [107] Ibid [108] Fig. 4.9 Alenquer House, Portugal, Aires Mateus. View of the diffusion of light on the white volumes. [online]. Available from: http://twobo.blogspot.com/2010/ [Accessed 5 July 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

support and value the theoretical and

geometrical substance within. It is an

philosophical fundament underpinning

expression of a dialogue between the

our design proposal. Porosity becomes

physical object and the space outside

not only a functional premise, but also a

and inside it, where the object penetrates

philosophical language aimed at defining

the surrounding environment and the

space and giving it character and vitality.

environment

permeates

the

object,

Hence, when we asked ourselves:

and, finally, the observer becomes an

is our research of porosity a desire of

integral part of such a harmonious and

emptiness and space as the protagonist of

extraordinary discourse.

architecture, or pursuit of the equilibrium

In conclusion, our design research was

of forms expressed through matter and

not focused on establishing the most

afterwards lightened by the voids? The

appealing configuration of the voids and

answer was: none of them. We aimed

porosity pattern. Above all else, it aspired

at creating an interactive architectural

to offer a unique space-time experience

proposal, where space and matter converse

where the design becomes only the

with each other. Much as in Aires Mateusâ&#x20AC;&#x2122;

prompt of a transcendental perception

architecture, in our project the voids, both

and metaphysical imagination which

shaded and illuminated cavities, model a

enables the spectator to go beyond the

dynamic and multi-directional space and

limits of the visible and palpable reality.

matter, able to captivate and involve the observer. Our wall does not only want to be the tangible display of an architectural language intended to demonstrate the multiple advantages of porosity. And even less, it means to be mere a contemplation of a combination of material technology and aesthetic language. Primarily, our architectural chunk wants to actualise a physical, visual and emotional relation with a space constituting unity with the 52

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

POROSITY AS A PROCESS

In the same way the question of whether

really and necessarily dependant on the

our

ontological determination of the idea of

interpreted as exaltation of space or search

porosity? Instinctively, the answer to the

of lightened materiality, another argument,

last question would be no, if we wanted to

immediately consequent to the first one, is

conform to the statement made in the last

posed: what is the process generating such

two paragraphs of the previous Chapter. In

a porosity configuration? Is it a growing

actual fact, the design process inevitably

process, an addition of geometric elements,

raised those questions, posing the issue

in accordance with the idea of porosity as

of the type of operations and techniques

a balanced disposition of forms which,

to follow in order to attain our desired

occasionally, break their contiguity with

outcome.

design

porosity

should

predetermined voids? Is it a subtracting

I will try to argue the introduced topic

procedure, where what is designed is

and

provide

the voids, the emptiness, achieved by a

gradual removal of insignificant matter?

methodologies employed during the

Or is it predetermined pattern, which

â&#x20AC;&#x153;challenge of designing porosityâ&#x20AC;?, with all

could change by varying the originating

their implications and connections with

factors? Are those types of methods

other disciplines.

illustrating

plausible the

explanations

approaches

and

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

Although appearing a theoretical and

according to the typology of pre-set

quite abstract matter, it transpired to be

inputs and constraints. Hence, the use of

pervaded by scientific and mathematical

Grasshopper, a plug-in of Rhinoceros, has

problematics. In fact, the purpose of our

been of great significance in executing this

research is not simply â&#x20AC;&#x153;designing porosityâ&#x20AC;?,

kind of research.

but rather pursuing strategies able to guarantee parametric control of the

5.1 Porosity as act of adding

design. This represents the opportunity

The initial attempt to construct a

configuration

parametric porosity language involved

indefinitely, continually ensuring the

the first solution of a component we

rationality, correctness and feasibility of

proposed for what was defined in Chapter

it. More technically, this means allowing

3 as the first layer of porosity. Our primary

innumerable chances of variation of each

modular geometry consisted of basic

single parameter, which can possibly

discrete components derived from the

be combined with likewise mutations of

aggregation of two or more voxel cubes

all other variable parameters in a given

(Fig. 5.1). Based on this, the strategies to

mathematical expression.

develop a rational design of porosity were

vary

the

design

To translate this notion into a real project

rather limited. The discrete geometries

we had to draw upon specific software able

were only suitable for an assembly process

to identify, develop and solve appropriate

with the features of a random growth. We

mathematical formulas or algorithms,

elaborated a script where the originating

Fig. 5.1: Basic discrete components derived from the aggregation of voxel cubes

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

point was represented by a predefined

allowed the rotation of the geometries of

set of starting geometries. More exactly,

90° , 180° , 360°in X, Y, Z directions so as to

six different discrete components derived

create dynamism in the growth. Secondly,

from the Rubik’s Cube puzzle. The function

we needed to define a rule of overlap

of the script was to build a growing process

ensuring the stability of the process. This

by overlapping alternatively and randomly

rule established that the growth occurs

the six basic components. However, in

by overlapping the components vertically,

order to guarantee rationality, stability and

with at least one entire face leaning against

manageability of growth, it was essential

the top surface of the underlying element

to input variable parameters, in the form

(Fig. 5.2). Finally, based upon a stability

of mathematical functions, as binding

criterion, the script should have selected,

and guiding assumptions. First of all, we

from time to time, the most suitable

LOGIC OF GROWTH

CHANGING PARAMETERS

SCRIPT

Fig. 5.2: Rules and changing parameters of the first script to guarantee at least one face overlapping the top surface of the underlying component

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

component and rotation (Fig. 5.3). Since the first trial presumed a random

yet and, on account of this, was not able to reach any appealing and reasonable result.

growth starting from one point - one component - resulting in a mediocre

5.2 Porosity as act of subtracting

column-like overall shape, we modified the

Not only did we need to rationalise the

script to recognise multiple components

process but also optimise the component

as starting points, variably displaced. The

itself. For this reason, we reoriented the

outcome was, apparently, a satisfying

strategy toward a cubic modular system,

organically-shaped porous wall, but, in

abandoning the discrete component

actual fact, it was composed of a series of

approach. Working with a cube module

separated and non-integrated multiple

meant drawing upon a 3d rectangular

columns of overlapping components (Fig.

grid as an invaluable method to control the

5.4).

directionality of growth. That also entailed

Clearly, the design was not under control

the necessity of figuring and designing

Fig. 5.3: Outcome of the first script based on the overlapping of components from one point 57

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Fig. 5.4: Outcome of the first script based on the overlapping of components from multiple points

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

porosity within the cube itself. Hence, the

permitting multiple rotations, in order to

second stages of the first layer of porosity

perceive more variability, and ensuring an

design took place, leading to a completely

adequate percentage of touching surfaces,

innovated configuration of our cubic

for the structural stability (Fig. 5.5) (Fig.

module (refer to Chapter 3). The new script,

5.6). Secondly, it generated porosity as a

devised ad hoc for the redesigned porous

subtracting process by gradually removing

modules, firstly guided the positioning

single components from the filled grid.

of the modules into the 3d grid, still

This subtraction method was developed

STARTING GEOMETRY

LOGIC OF GROWTH

Fig. 5.5: Logic of growth of the new modular geometry for the randome reduce script STARTING GEOMETRY

LOGIC OF GROWTH

Fig. 5.6: Logic of growth of the new modular geometry for the shortest walk script 59

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

to occur in two different ways. In one case,

shortest walk, along which to operate the

it implied a simple random reduce, letting

reduction of the elements. In this specific

the script randomly select the components

case, the act of subtracting should interest

to be deleted (Fig. 5.7) (Fig. 5.8). In the

only the components further from the

other, we figured a series of paths, called

shortest walk, avoiding the ones along and

LOGIC OF SUBTRACTION

CHANGING PARAMETERS

SCRIPT

Fig. 5.7: Changing parameter and logic of subtraction in the random reduce script

Fig. 5.8: Randome reduce outcome 60

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

close to the paths (Fig. 5.9) (Fig. 5.10).

through

Despite the improvement accomplished LOGIC OF SUBTRACTION

this

second

attempt,

designing process proved to be still too CHANGING PARAMETERS

SCRIPT

Fig. 5.9: Changing parameter and logic of subtraction in the shortest walk script

Fig. 5.10: Shortest walk outcome

the

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

random, with an aesthetical outcome

algorithm which allowed us to not only

somewhat repetitive and flat. In reality, our

design more complex porosity within

design research was aimed at achieving

each module - 256 variations (refer to

the opposite result: creating a highly

Chapter 3) -, but also to follow specific

changeable configuration of porosity,

arrangements of the modules, based on

which apparently seems random in its

predefined patterns, through the control

variability and dynamism, but, in fact, is

of their vertices. The pattern was designed

completely under the control of parametric

using Curl-noise, a specific function of

means.

Grasshopper, and represented as surfaces within a rectangular grid of points.

5.3 Porosity as pattern Therefore,

the

awareness

Depending on whether the points of the of

the

grid were outside or inside those surfaces,

necessity for a different strategy became

the Marching Cube algorithm was able to

determinant. We demanded full control

identify the corresponding marching cube

and to be able to decide and vary the

module for each cell of the grid and place

position of the modules and the voids in

it appropriately (Fig. 5.11) (Fig. 5.12).

the wall, depending on external functional or aesthetic factors.

The outcomes of the new strategy proved to be pleasingly satisfying (Fig.

The only way to guarantee such a

5.13), although some issues seemed

manipulating role was to design and

to be still unsolved. Issues relating to

predetermine a pattern of the overall

the control of the boundaries and the

porosity configuration and make the

structural performance of the overall

modules follow it. However, we had

proposal. In-fact Curl-noise was unable to

to ensure this interconnectivity and

recognise the edges of the wall, causing

dependence of the position of the

discontinuity along the boundaries and

modules on the pattern for all the infinite

structural instability of the surrounding

variations of the pattern itself. For this

parts of the wall (Fig. 5.14). These concerns

reason, we drew upon the Marching Cube

established the final step of this design

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

CHANGING PARAMETERS

SCRIPT

Fig. 5.11: Changing parameter and Marching Cube script

Fig. 5.12: Process of defining porosity configuration from the pattern generated by Curlnoise

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Fig. 5.13: Proposal deriving from the Marching Cube script

research, connoted by the use of the

longer Curl-noise; instead, Voronoi. The

Voronoi diagram.

Voronoi Diagram is a mathematical formula

The ideation of a pattern for the porosity

which divides the space into regions

configuration was still a fundamental

depending on the distance between all

prerequisite. What changed was the

points of that space and a set of specific

parametric function generating it: no

and predetermined points, called seed[109].

Fig. 5.14: Different control of the boundaries between Curl-noise (left) and Voronoi (right) [109]â&#x20AC;&#x192;Wikipedia. 4 July 2018. Voronoi diagram, [online]. Available from: https://en.wikipedia.org/wiki/Voronoi_diagram [Accessed 8 July 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

Therefore, each region is composed of all the points of the space closest to the specific point of the seed present in that region (Fig. 5.15). Nowadays, the Voronoi diagram is broadly used in architecture and urban design, as it contributes to achieving more organic forms and naturallooking patterns[110] (Fig. 5.16) (Fig. 5.17). The same contribution was also provided to our design. By defining a bounding box (corresponding to the volume of the wall), a seed of points and converting the boundary lines of the formed regions, resulting from the Voronoi partitioning, into

three-dimensional

meshes,

Fig. 5.15: Examples of Voronoi diagrams[111]

the

achievement of dynamic and organic

Fig. 5.16: National Kaohsiung Performing Arts Center, Zaha Hadid proposal[112]

Fig. 5.17: Water Cube for Beijing 2008 Olympic Games by PTW Architects[113]

[110] Sahin, A. 5 July 2017. Examining the use of voronoi diagrams in architecture on a student project. [online]. Available from: https://www.researchgate.net/publication/318208318_EXAMINING_THE_USE_OF_VORONOI_ DIAGRAMS_IN_ARCHITECTURE_ON_A_STUDENT_PROJECT [Accessed 8 July 2018] [111] Fig. 5.15 Examples of Voronoi diagrams. [online]. Available from: https://github.com/d3/d3-voronoi [Accessed 9 July 2018] [112] Fig. 5.16 National Kaohsiung Performing Arts Center, Zaha Hadid proposal. [online]. Available from: https://www. researchgate.net/publication/318208318_EXAMINING_THE_USE_OF_VORONOI_DIAGRAMS_IN_ARCHITECTURE_ON_A_ STUDENT_PROJECT [Accessed 8 July 2018] [113] Fig. 5.17 Water Cube for Beijing 2008 Olympic Games by PTW Architects. Ibid

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

porosity

configurations

was

finally

tangible (Fig. 5.18) (Fig. 5.20). Moreover,

borderline arrangements along the edges or structural uncertainties (Fig. 5.19).

we attained utter control of the direction

Regardless of the technical implications

and evolution of the design, no longer with

and the consequences derived from the

Boundary

Point cloud

Voronoi cells

T-spline mesh

Fig. 5.18: Voronoi generation

Fig. 5.19: Optimization of the boundaries of the wall with the Voronoi script

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

Fig. 5.20: The porosity configuration resulting from the Voronoi script

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

digital issues in the design of porosity, it

keeps growing to infinity or stops when

would be interesting, in my opinion, to

assigning limits? Vice versa, does not a

conclude the discourse by reconnecting

growing addition of the same element

with the theoretical premises alluded to

generate a pattern itself? Therefore, is

in the introduction of the Chapter.

it sensible to identify the most efficient

The design of porosity has been

solution in terms of architectural design?

presented in this Chapter as a growing,

Gothic Architecture actualized a gradual

subtracting or a preconfigured pattern.

reduction and lightening of the masses

How can we identify the correct method

of the Romanesque. It represented a

for generating porosity? Are they really

revolutionary process of the subtraction

divergent? Also, what is effectively a

of matter, stimulated by both theoretical,

pattern? In most dictionaries pattern is

religious and structural reasons, which

defined as “an arrangement of repeated

led to its acme, when architecture

parts or decorative designs”.[114] Sometimes

became “a bundle of bones, fibre and

it is specified that it is a repetition of

muscles, a structural skeleton covered by

elements “in a predictable manner”[115].

unsubstantial cartilage.” (Bruno Zevi, 1957)

But if this is real, is not the pattern actually

[116]

a process of adding or subtracting which

. The result was astonishing (Fig. 5.21).

In the Simmons Hall dormitory, MIT,

Fig. 5.21: Example of slender structure of Gothic

architecture. Cathedral Basilica of Our Lady of Amiens[117] [114] Thomson, M., (2008). Collins English Dictionary. Glasgow: HarperCollins Publishers [115] Wikipedia, 5 May 2018. Pattern. [online]. Available from: https://en.wikipedia.org/wiki/Pattern [Accessed 9 July 2018) [116] Zevi, B., (1957) Architecture as space, New York: Horizon Press. [117] Fig. 5.21 Example of slender structure of Gothic architecture. [online]. Available from: https://www.quora.com/ What-should-everyone-know-about-Gothic-Architecture [Accessed 9 July 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

Steven Holl Architects aimed at realising “overall urban porosity”[118] inspired by the model of the sponge. They achieved porosity on the facades by implementing the

two-dimensional

fractal

the

Sierpinski carpet, more exactly its three-

Fig. 5.22: The Menger sponge research for

the porosity of the facade of the immons Hall dormitory, MIT, Steven Holl Arhcitects[120]

dimensional version the Menger Sponge. This consists: “a plane, square in shape, is divided in 3 × 3 = 9 congruent squares, b) the center square is removed. This treatment applies recursively to the remaining 8 squares and it may continue indefinitely. A 3-dimentional version of the

Fig. 5.23: The facade of the Simmons Hall dormitory, MIT, Steven Holl Arhcitects[121]

Sierpinski carpet, involving cubes instead

distinction divides all the approached

of squares, forms the Menger sponge.”[119]

solutions and a strong sense of relativity

(Fig. 5.22) The porosity outcome was

pervades and influences the discourse.

outstanding (Fig. 5.23). Was it not an

Much as relativity in the perception

operation of division and subtraction

of space and time, we would need to

originating, ultimately, a pattern? The

acknowledge the relativity of the analysis

answer is yes.

and interpretations of the porosity

Thence, it becomes evident how different

design. All we can do is to keep exploring

processes and designing strategies can

strategies and approaches, contextualising

be equally successful depending on the

and evaluating the outcomes according to

particular circumstances.

the relative and specific circumstances.

In actual fact, an extremely subtle

[118] Kotsopoulos, S. D. 2007. Design Concepts in Architecture: The Porosity Paradigm. International Journal of architectural computing. [online]. 06(03), pp. 337-358. Available from https://www.researchgate.net/ publication/221467193_Design_Concepts_in_Architecture_the_Porosity_Paradigm? [Accessed 10 May 2018] [119] Ibid [120] Fig. 5.22 The Menger sponge research for the porosity of the facade of the immons Hall dormitory, MIT, Steven Holl Arhcitects. Available from https://www.researchgate.net/publication/221467193_Design_Concepts_in_ Architecture_the_Porosity_Paradigm? [Accessed 10 May 2018] [121] Fig. 5.23 The facade of the Simmons Hall dormitory, MIT, Steven Holl Arhcitects. [online]. Available from: http:// arkitekt-ur.blogspot.com/2013/11/mit-simmons-hall-by-steven-holl.html [Accessed 6 July 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

THE BOUNDARIES OF POROSITY

Another significantly intricate issue, which

the design of the pattern, improving the

has addressed further lines of investigation,

structural stability of the borderline areas.

is the contradictory idea of boundaries as

However,

limit of growth of our porous architectural

realistically,

language.

proposal, a wall, implies, we can instantly

what

consider, our

architectural

Regarding the technical sphere, in the

understand the entity of the inconsistency.

previous Chapter the disadvantages

The English Oxford Living Dictionaries

deriving from the use of Curl-noise to

defines a wall as “a continuous vertical

design the porosity pattern were already

brick or stone structure that encloses or

explained. Not being able to identify the

divides an area of land.”[122]. The words

edges of the grid representing the wall,

“continuous”, “encloses” and “divides”

caused discontinuity in the body of the wall

here clearly embody an idea of separation,

along the boundaries and, consequently,

uninterrupted

structural problems. Instead, by using the

a defined object and its undefined

Voronoi function, we could assure the

surrounding. But such an idea is not only

involvement of all parts of the grid into

typical of a semantic description in a

demarcation

between

[122] English Oxford Living Dictionary. 2018. Etymology and definition of the word wall. [online]. Available from: https:// en.oxforddictionaries.com/definition/wall [Accessed 26 April 2018]

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

dictionary. The perception of a wall as an instrument of closure and marking out is inherent in human nature. Throughout history, walls, very often combined with castles or strongholds, have been means of ensuring defence and safety from contingent menace of hostile populations. Regarding this, it is worth recalling the construction of massive walls, realised

Fig. 6.1: Muraille Aurelien Walls, Rome[124]

by the Romans to fortify their military camps and cities, and the noticeably long operation of the erection of the Great Wall, in China, with the multiple purposes of protection from military attacks, raids and border control[123] (Fig. 6.1) (Fig. 6.2). Looking at the more modern world, the wall that, par excellence, has represented a symbol of closure, division and obstruction

Fig. 6.2: Great Wall, China[125]

is the Berlin Wall (Fig. 6.3). Nothing, in modern European culture, has meant impenetrability, solid separation and clear boundary more than it has. Aristotle, in book V of his Metaphysics, defines the concept of limit (πέραs) as the extreme boundary of all bodies; it

Fig. 6.3: Berlin Wall[126]

is the entity which distinguishes the here, where the whole body is manifested, and

[123] Crystalinks. 2015. The Great Wall of China. [online]. Available from: http://www.crystalinks.com/greatwallofchina. html [Accessed 8 July 2018] [124] Fig. 6.1 Muraille Aurelien Walls, Rome. [online]. Available from:[online]. Available from: https://en.wikipedia.org/ wiki/Defensive_wall [Accessed 8 July 2018][Accessed 8 July 2018] [125] Fig. 6.2 Great Wall, China. [online]. Available from: https://en.wikipedia.org/wiki/Defensive_wall [Accessed 8 July 2018] [126] Fig. 6.3 Berlin Wall. [online]. Available from: https://www.pinterest.at/pin/415316396866722600/ [Accessed 7 May 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

the beyond, where the body does not exist

sharp and strong belief, be undermined

at all[127]. According to Aristotle, the limit is

and overturned so as to acquire its opposite

what separates the inside from the outside.

significance? How could it be an expression

This is also what Gaston Bachelard (1958)

of the indefinite, allusion to distant infinite,

reveals in his The dialectics of outside

and, implicitly, a link to something beyond

and inside[128]. “Outside and inside form

our sight and tangibility? Indeed, the

a dialectic of division”[129]. It is extremely

application of porosity language to the

touching when, referring to the example

traditional architectural manifestation of

of various poems, he raises the theme of

the wall would subvert its main features,

the threshold: “there are two beings in

expression of solidity, massiveness and

a door, that a door awakens in us a two-

impenetrability.

way dream, that it is doubly symbolical.

and vehicle of division it would become

And then, onto what, toward what, do

a filter, an architectural object able to

doors open? Do they open for the world

generate a two-way communication

of men, or for the world of solitude?”[130]

between contiguous places with different

Amazingly, with these words, the author

peculiarities, two disparate realities on its

seems to recall in one sentence the years

opposite sides. This would entail not only

of hope, dreams and fears of those people

the passage of air and water through it, but

separated by the monster of the Berlin

also an impressive transition of light and

Wall.

sounds and, most importantly, a “romantic”

Hence,

from

barrier

By virtue of all this, a spontaneous

flow of views and visions of the unknown

questioning arises: how could such a

beyond. Giacomo Leopardi in its “Infinito”

substantial symbol, which encloses a very

writes:[131]

[127] Ulliana, S., 12 January 2017. Aristotele, Metafisica. [online]. Available from: https://www.researchgate.net/ publication/312220245_Aristotele_Metafisica_A_Sintesi_e_commento_personale_al_libro [Accessed 8 July 2018] [128] Bachelard, G., (1958). The dialectics of outside and inside. In: Bachelard, G., The poetics of space. Boston: Beacon Press [129] Ibid [130] Ibid [131] Leopardi, G., (1974), “L’infinito”, in G. Einaudi (ed.), I Canti, Milano: Rizzoli: XII. 1-8

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

Always dear to me was this solitary hill and this hedge, which, from so many parts of the far horizon, the sight excludes. But sitting and gazing endless spaces beyond it, and inhuman silences, and the deepest quiet, I fake myself in my thoughts; where almost my heart scares[132]

which some of these flows and programs penetrate the site”[135]. All these considerations have subtended the theoretical and philosophical approach of our design proposal. Supposing we wanted to connect such a theoretical speculation on the theme of boundaries with the discourse concerning

Similarly to the hedge which, in the

the interpretation of porosity as a process.

“Infinito”, excludes a clear sight of the world

The conception of boundary as a limit

beyond it and, that being so, inspires the

acquires a relevance here as it has never

imagination of the infinite of the horizon,

had before. If we consider the real moment

a porous wall, offering numerous glimpses

of the conception of porosity as an act of

through multifarious interstices, induces

growth, subtraction or as a pattern, which

human beings to experience the pleasant

could, potentially, develop to infinite, it is

perception of the elusive beyond.

immediate the acknowledgment of the

On the urban scale, the term boundaries

necessity of an end, a limit identifying

would change into borders, as alive

the interruption of the process. Thence,

delimitations,

interchange,

the subsequent question would be: is

which identify those areas where the

it possible to impose that limit in such a

urban porosity occurs[133]. The sociologist

virtual context of design? The answer is

Richard Sennet, engaged with the issue

positive and the medium to obtain that

of the distinction between boundaries

can only be represented by mathematical

and borders, defines boundaries as “dead

formulas or algorithms to input in the

ends”[134], in opposition to border which

script to force the process to stop. This

“is an edge, which is active and allows

was the strategy we undertook which,

coexistence. It permits interfaces, through

more specifically, consisted of building

open

[132] Reed, H., 1 October 2016. The infinite. [online]. Available from: http://www.solearabiantree.net/namingofparts/ infinite.php [Accessed 27 April 2018] [133] Stratis, S. 2012. Creating a porous urban connective tissue. [online]. Available from: http://admin.brainserver. net/uploads/aau/projects/ARTICLES/ARTICLES_BY_SOCRATES_STRATIS_/WelcomeBackToMyBackYard/ WelcomeBackInMyBackYard.pdf [Accessed 7 July 2017] [134] Ibid [135] Ibid

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

a bounding box, containing the future

designer in the control and development

virtual wall, and identifying it as the limits

of the project. The digital and parametric

of the pattern design through algorithmic

resource constitutes only the powerful

functions (Fig. 6.4).

means

subjected

the

decisional

This experience once again emphasizes

orientation and creativity of the designer.

the crucial and decisive role of the

The last argument I would like to raise

BOUNDING BOX

VORONOI CONFIGURATION GENERATED WITHIN THE BOUNDING BOX

OPTIMIZATION OF THE MESHES GENERATED BY VORONOI

THE WALL CONTAINED IN THE BOUNDING BOX

Fig. 6.4: Definition of the boundaries of the porosity configuration through a bounding box

around the topic of boundaries will prove

of porosity was fictitious, mere appearance

to be particularly intriguing and slightly

and simulation of porosity, would it still

insidious, almost leading the discourse

be relevant to define its boundaries? If

to another dialectical topic, porosity as

the porous brick wall suddenly started

ornamentation or function. If the pattern

dissolving, turning into a mere aggregation

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

of glass bricks, would it still be reasonable

porosity? (Fig. 6.5) (Fig. 6.6)

to talk about porosity and boundaries of

Fig. 6.5: Crystal Houses, Amsterdam, MVRDV[137]

Fig. 6.6: Detail of Crystal Houses, Amsterdam, MVRDV[138]

Even worse, if the porous configuration

cladding[136], would it still be proper to

were only a fake result of a simple collage

discuss it as design of porosity boundaries?

of brick-built images printed on glass

(Fig. 6.7) (Fig. 6.8)

Fig. 6.7: Glass Farm, Schijndel, MVRDV[139]

Fig. 6.8: Detail of Glass Farm, Schijndel, MVRDV[140]

[136] Delicado, G. H. and Marcos, M. J., 27 February 2013. Glass farm. MVRDV. [online]. Available from: http://www. abitare.it/en/architecture/2013/02/27/glass-farm-mvrdv/ [Accessed 8 July 2018] [137] Fig. 6.5 Crystal Houses, Amsterdam, MVRDV. [online]. Available from: http://www.talkiesmagazine.nl/news/ fashion/chanel-temporary-boutique/ [Accessed 9 July 2018] [138] Fig. 6.6 Detail of Crystal Houses, Amsterdam, MVRDV. [online]. Available from: http://www.talkiesmagazine.nl/ news/fashion/chanel-temporary-boutique/ [Accessed 9 July 2018] [139] Fig. 6.7 Glass Farm, Schijndel, MVRDV. [online]. Available from: http://www.abitare.it/en/architecture/2013/02/27/ glass-farm-mvrdv/ [Accessed 9 July 2018] [140] Fig. 6.8 Detail of Glass Farm, Schijndel, MVRDV. [online]. Available from: http://www.abitare.it/en/ architecture/2013/02/27/glass-farm-mvrdv/ [Accessed 9 July 2018]

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

In my opinion, these examples should, more suitably, be ascribed to the subject mentioned

above,

concerning

mere theoretical speculation not pertinent to our research.

the

In fact, this particular debate has never

contraposition of the porosity design

involved our design research. The latter

as pure ornamentation or function.

has always been demonstrated as a result

This topic has been evoked in different

of the progressive interdependence and

occasions throughout the report but will

integration between the two faces of the

not be deepened further. This choice is

concept of porosity, functionality and

motivated by the reasonable will to avoid

aesthetic value.

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

CONCLUSION

Some of the major issues faced in the contemporary

world

architecture

can be identified as follows. Necessity of

simplification

The architectural research described in this report endeavoured to respond to

systems, returning to the essentiality

those requirements with a sensible and

and

elements

realistic proposal. Learning from nature,

and mechanisms. Demand of flexible,

the design investigation borrowed one

complex and competitive architectural

of the most common and primordial

solutions imposed by the development

characteristics, porosity, transposing it

of sophisticated means of parametric

onto the architectural field. It explored the

design and the spreading of cutting-edge

concept of porosity on different levels to

digital technologies. Constant yearning

guarantee its application on multiple scales.

for beauty, dictated by the ideal of

It conceived a new architectural language,

unicity, exceptionality and astonishment.

based on the iteration and modularity of the

The modern idea of beauty seems to be

components, to ensure mass production

accomplished by the perfect equilibrium

and feasibility. Furthermore, it satisfied

processes

symmetry and chaos.

and

efficiency

between rationality and randomness,

natural

The language of porosity: rational randomness. Versatility of innovative and modular clay geometries.

the desire of innovation and originality

terms of flexibility, structural performance,

through the design of elegant and unique

efficiency and aesthetic quality.

three-dimensional

clay

components,

To conclude, the value of this design

which appear to outshine the traditional

research lies in its capability and further

two-dimensional brick wall and unfold

perspective to elevate a primordial and

new perspectives of development of the

natural property and material such as

architectural clay systems. The engine

porosity and clay to highly-technological

of the design development consisted

and versatile applications, offering an

of specific parametric software which

innovative,

allowed the optimization of the proposal in

architectural language.

parametric

and

unique

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

The language of porosity: rational randomness.

Versatility of innovative and modular clay geometries.

OUTLOOK

This proposal is not meant to be the answer, the final solution and the end. It represents only the initial point of a new highly potential field of exploration. Unquestionably, many aspects should be further developed and optimised. However, starting from the knowledge and awareness acquired through this research, invaluable and crucial innovative solutions could be achieved.

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• • • 85

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LIST OF FIGURES Abstract

Fig. 0: Clay geometry fabricated with the slip-casting technique. Author’s own image

1. Introduction

Fig. 1.1: Proposal for an architectural application of our modular and porous clay language. Author’s own image

2. Different scale of porosity

Fig. 2.1: Cross-sectional image of composite oxide ceramics, a low-porosity material. [online]. Available from: https://www.sciencedirect.com/science/article/pii/B9780124077881000010#s0015 [Accessed 17 June 2018] Fig. 2.2: Two-dimensional reticulated materials with square pores. [online]. Available from: https:// www.sciencedirect.com/science/article/pii/B9780124077881000010#s0015 [Accessed 17 June 2018] Fig. 2.3: Three-dimensional reticulated foamed materials: nickel foam and iron foam. [online]. Available from: https://www.sciencedirect.com/science/article/pii/B9780124077881000010#s0015 [Accessed 17 June 2018] Fig. 2.4: Representative examples of metallic foams prepared either by direct (a and b) or by indirect (c and d) foaming techniques. [online]. Available from: http://pubs.rsc.org/en/Content/ ArticleHtml/2015/MH/c4mh00244j [Accessed 18 April 2018] Fig. 2.5: Representative examples of metal sponges prepared by different routes. [online]. Available from: http://pubs.rsc.org/en/Content/ArticleHtml/2015/MH/c4mh00244j [Accessed 18 April 2018] Fig. 2.6: Representative examples of nanoporous metals. [online]. Available from: http://pubs.rsc. org/en/Content/ArticleHtml/2015/MH/c4mh00244j [Accessed 18 April 2018] Fig. 2.7: Examples of application of porous aluminium. [online]. Available from: https://www. exxentis.com/anwendungen/ [Accessed 19 April 2018] Fig. 2.8: Examples of clay applications: bricks, floor tiles and roof tiles. [online]. Available from: http://www.ugabox.com/business/directory/clay-products.html [Accessed 6 July 2018] Fig. 2.9: Examples of usage of ceramics. Lydia johnson ceramics. [online]. Available from: http:// e2.turningearth.uk/lydia-johnson/ [Accessed 6 July 2018] Fig. 2.10: Example of perpendicularity of plans in the neoplasticism architecture. Theo van Doesburg Contra-Construction Project (Axonometric) 1923. [online] Available from: https://www. moma.org/collection/works/232 [Accessed 7 July 2018] Fig. 2.11: Model of Maison Particulière (Private House), Theo van Doesburg and Cornelis van Eesteren. [online]. Availabe from: https://it.pinterest.com/zlatko928/620-bauhaus-de-stijlneoplasticism/?lp=true [Accessed 7 July 2018] Fig. 2.12: Simmons Hall dormitory, MIT, Steven Holl Architects. [online]. Available from: http:// arkitekt-ur.blogspot.com/2013/11/mit-simmons-hall-by-steven-holl.html [Accessed 6 July 2018] Fig. 2.13: Study for the application of horizontal and vertical porosity. Simmons Hall, MIT. [online] Available from: https://www.e-architect.co.uk/boston/simmons-hall-boston [Accessed 12 May 2018] Fig. 2.14: Outcome of the vertical and horizontal porosity design. Simmons Hall, MIT. [online] Available from: https://www.e-architect.co.uk/boston/simmons-hall-boston [Accessed 12 May 2018] Fig. 2.15: Sketch for the porosity on the facade. Simmons Hall, MIT. [online]. Available from: http:// 87

arkitekt-ur.blogspot.com/2013/11/mit-simmons-hall-by-steven-holl.html [Accessed 12 May 2018] Fig. 2.16: Outcome of the porous facade through the multitute of windows. Simmons Hall, MIT. [online]. Available from: http://arkitekt-ur.blogspot.com/2013/11/mit-simmons-hall-by-steven-holl. html [Accessed 12 May 2018] Fig. 2.17: Sketch for the vertical cavities. Simmons Hall, MIT. [online]. Available from: http:// arkitekt-ur.blogspot.com/2013/11/mit-simmons-hall-by-steven-holl.html [Accessed 12 May 2018] Fig. 2.18: Detail of the vertical porosity through the cavities. Simmons Hall, MIT. [online]. Available from: http://arkitekt-ur.blogspot.com/2013/11/mit-simmons-hall-by-steven-holl.html [Accessed 12 May 2018] Fig. 2.19: Slum Housing in El Salvador. [online]. Available from https://www.povertyactionlab.org/ evaluation/slum-housing-upgrading-el-salvador-mexico-and-uruguay [Accessed 7 July 2018] Fig. 2.20: Favela housing in Rio de Janeiro. Picture by Paul Stallan. [online]. Available from https:// www.urbanrealm.com/blogs/index.php/2011/05/23/slum-jpg?blog=12 [Accessed 7 July 2018] Fig. 2.21: Sponge City, Peter Cook 1974. [online]. Available from: https://onlinelibrary.wiley.com/ doi/pdf/10.1002/ad.419 [Accessed 18 April 2018] Fig. 2.22: Section of the Sponge City project, Peter Cook 1974. [online]. Available from: https:// onlinelibrary.wiley.com/doi/pdf/10.1002/ad.419 [Accessed 18 April 2018] Fig. 2.23: Porous wall. Architectural scale. Author’s own image Fig. 2.24: Cross-scale design development. Author’s own image Fig. 2.25: The porous skyscraper. Author’s own image Fig. 2.26: The metal frame as a support of the light clay shading system. Author’s own image Fig. 2.27: Application of the structural solid components as a pavilion. Author’s own image

3. Different layers of porosity

Fig. 3.1: Coloured scanning electron micrograph (SEM) of a leaf tissue structure. [online]. Available from: https://fineartamwww/featured/leaf-tissue-structure-sem-steve-gschmeissner.html [Accessed 18 June 2018] Fig. 3.2: Different layers of a leaf tissue structure. [online]. Available from: https: https://www. slideshare.net/j0martin/plant-tissues-and-organs [Accessed 18 June 2018] Fig. 3.3: Example of shadow in architectural patio. [online]. Available from: https://www.loverush. com.au/la-belle-vie/ [Accessed 18 June 2018] Fig. 3.4: Effect of sunlight passing through a porous wall. San Telmo Museum, San Sebastian, Nieto Sobejano Arquitectos. [online]. Available from: https://www.archdaily.com/208764/santelmo-museum-nieto-sobejano-arquitectos [Accessed 18 June 2018] Fig. 3.5: Possibilities of components depending on the number of cubes aggregated. Author’s own image Fig. 3.6: One example of the solutions of Soma cube. [online]. Available from: https://en.wikipedia. org/wiki/Soma_cube [Accessed 18 June 2018] Fig. 3.7: Examples of monocube, dicubes, tricubes, tetracubes, pentacubes and hexacubes for Baiocchi Figures. [online]. Available from: http://www.recmath.org/PolyCur/besbaiocchi/index. html [Accessed 14 February 2018] Fig. 3.8: Outcome of the combination of the first solutions of porous modules. Author’s own image Fig. 3.9: Some of 256 configurations of the cubic module, obtained by intersecting the cube with a sphere, following the marching cube logic. Author’s own image Fig. 3.10: Application of the marching cube subtracting process to the polycubes. Author’s own image Fig. 3.11: Application of the marching cube subtracting process to the polycubes. Author’s own image Fig. 3.12: Ennis House, Frank Lloyd Wright, Los Angeles, California. [online]. Available from: https:// whiteriver.com/products/cube-paperweight-ennis-design-2-5-sq [Accessed 9 May 2018] Fig. 3.13: La Miniatura, Frank Lloyd Wright, Los Angeles, California. [online]. Available from: http:// www.sytyson.com/storer-house-par-frank-lloyd-wright/ [Accessed 9 May 2018] Fig. 3.14: Some examples of the module cut following the pattern of lines. Author’s own image

Fig. 3.15: Two examples of combination of different modules cut according to the pattern of lines. Author’s own image Fig. 3.16: Final geometry. Author’s own image Fig. 3.17: Final geometry in the overal design. Author’s own image Fig. 3.18: The benefits of a porous wall. Author’s own image Fig. 3.19: Variation of the second layer of porosity through the parametric control of its design. Author’s own image Fig. 3.20: Example of marine sponges: Phylum Porifera. [online]. Available from: https:// thephylumporiferaproject.wikispaces.com/Callyspongia+plicifera [Accessed 8 July 2018] Fig. 3.21: Examples of Mashrabiya serving as ventilation and protection for buildings. [online]. Available from: https://www.hommeg.com/moucharabieh-all-on-the-art-and-deco-piece-verytrendy [Accessed 4 July 2018] Fig. 3.22: Al Bahar Towers, Abu Dhabi, Aedas Architects. [online]. Available from: m/270592/albahar-towers-responsive-facade-aedascom/moucharabieh-all-on-the-art-and-deco-piece-verytrendy [Accessed 4 July 2018] Fig. 3.23: Larchmont Lotus Building, Los Angeles, XP& Architecture. [online]. Available from: https://archinect.com/firms/project/17201981/larchmond-lotus-xp-architecture-designs-aclimate-regulating-self-cleaning-and-image-improving-new-envelope-for-the-larchmontmedical-center-in-los-angeles/17201983 [Accessed 4 July 2018] Fig. 3.24: King Fahad National Library, Saudi Arabia, Gerber Architekten. [online]. Available from: https://it.pinterest.com/pin/489766528198435415/?lp=true [Accessed 4 July 2018] Fig. 3.25: Casa Walther Moreira Salles, Rio de Janeiro, Olavo Redig de Campos. [online]. Available from: https://belblasiarquitetura.wordpress.com/tag/arquitetura/ [Accessed 4 July 2018] Fig. 3.26: Termitary House, Thanh Khe District, Vietnam, Tropical Space. [online]. Available from: https://www.archdaily.com/594339/termitary-house-tropical-space [Accessed 4 July 2018]

4. Porosity in a dualism of space and matter

Fig. 4.1: Untitled (One Hundred Spaces) 1995 by Rachel Whiteread. [online]. Available from: http://www.artzip.org/rachel-whiteread [Accessed 24 May 2018] Fig. 4.2: Untitled (Book Corridors) 1998 by Rachel Whiteread. [online]. Available from: http:// www.tate.org.uk/art/artists/rachel-whiteread-2319/five-things-know-rachel-whiteread [Accessed 24 May 2018] Fig. 4.3: Untitled (Stairs), 2001 by Rachel Whiteread. [online]. Available from: http://www.tate.org. uk/art/artists/rachel-whiteread-2319/five-things-know-rachel-whiteread [Accessed 24 May 2018] Fig. 4.4: Relativity, 1953, by Maurits Cornelis Escher. [online]. Available at: http://artattack911. com/mc-escher-mind-bending-art-bay-area-and-peninsula-art-classes-for-all-ages/ [Accessed 24 May 2018] Fig. 4.5: The Prisons, 1750, Giovanni Battista Piranesi. [online]. Available at: https://en.wikipedia. org/wiki/Giovanni_Battista_Piranesi#The_Prisons_(Carceri) [Accessed 24 May 2018] Fig. 4.6: Ghost II, 2009 by Rachel Whiteread. [online]. Available from: http://www.artzip.org/ rachel-whiteread [Accessed 24 May 2018] Fig. 4.7: Alenquer House, Portugal, Aires Mateus. View of the openings toward the outside. [online]. Available from: http://arquitecturadesignetc.blogspot.com/2011/10/manuel-e-franciscoaires-mateus-casa-em.html [Accessed 5 July 2018] Fig. 4.8: Alenquer House, Portugal, Aires Mateus. Plan and an internal perspective view. [online]. Available from: http://twobo.blogspot.com/2010/ [Accessed 5 July 2018] Fig. 4.9: Alenquer House, Portugal, Aires Mateus. View of the diffusion of the light on the white volumes.. [online]. Available from: http://twobo.blogspot.com/2010/ [Accessed 5 July 2018]

5. Porosity as a process

Fig. 5.1: Basic discrete components derived from the aggregation of voxel cubes. Author’s own

image Fig. 5.2: Rules and changing parameters of the first script to guarantee at least one face overlapping the top surface of the underlying component. Author’s own image Fig. 5.3: Outcome of the first script based on the overlapping of components from one point. Author’s own image Fig. 5.4: Outcome of the first script based on the overlapping of components from multiple points. Author’s own image Fig. 5.5: Logic of growth of the new modular geometry for the randome reduce script. Author’s own image Fig. 5.6: Logic of growth of the new modular geometry for the shortest walk script. Author’s own image Fig. 5.7: Changing parameter and logic of subtraction in the random reduce script. Author’s own image Fig. 5.8: Randome reduce outcome. Author’s own image Fig. 5.9: Changing parameter and logic of subtraction in the shortest walk script. Author’s own image Fig. 5.10: Shortest walk outcome. Author’s own image Fig. 5.11: Changing parameter and Marching Cube script. Author’s own image Fig. 5.12: Process of defining porosity configuration from the pattern generated by Curl-noise. Author’s own image Fig. 5.13: Proposal deriving from the Marching Cube script. Author’s own image Fig. 5.14: Different control of the boundaries between Curl-noise (left) and Voronoi (right). Author’s own image Fig. 5.15: Examples of Voronoi diagrams. [online]. Available from: https://github.com/d3/d3voronoi [Accessed 9 July 2018] Fig. 5.16: National Kaohsiung Performing Arts Center, Zaha Hadid proposal. [online]. Available from: https://www.researchgate.net/publication/318208318_EXAMINING_THE_USE_OF_ VORONOI_DIAGRAMS_IN_ARCHITECTURE_ON_A_STUDENT_PROJECT [Accessed 8 July 2018] Fig. 5.17: Water Cube for Beijing 2008 Olympic Games by PTW Architects. [online]. Available from: https://www.researchgate.net/publication/318208318_EXAMINING_THE_USE_OF_ VORONOI_DIAGRAMS_IN_ARCHITECTURE_ON_A_STUDENT_PROJECT [Accessed 8 July 2018] Fig. 5.18: Voronoi generation. Author’s own image Fig. 5.19: Optimization of the boundaries of the wall with the Voronoi script. Author’s own image Fig. 5.20: The porosity configuration resulting from the Voronoi script. Author’s own image Fig. 5.21: Example of slender structure of Gothic architecture. Cathedral Basilica of Our Lady of Amiens. [online]. Available from: https://www.quora.com/What-should-everyone-know-aboutGothic-Architecture [Accessed 9 July 2018] Fig. 5.22: The Menger sponge research for the porosity of the facade of the immons Hall dormitory, MIT, Steven Holl Arhcitects. [online] Available from https://www.researchgate.net/ publication/221467193_Design_Concepts_in_Architecture_the_Porosity_Paradigm? [Accessed 10 May 2018] Fig. 5.23: The facade of the Simmons Hall dormitory, MIT, Steven Holl Arhcitects. [online]. Available from: http://arkitekt-ur.blogspot.com/2013/11/mit-simmons-hall-by-steven-holl.html [Accessed 6 July 2018]

6. The boundaries of porosity

Fig. 6.1: Muraille Aurelien Walls, Rome. [online]. Available from: https://en.wikipedia.org/wiki/ Defensive_wall [Accessed 8 July 2018][Accessed 8 July 2018] Fig. 6.2: Great Wall, China. [online]. Available from: https://en.wikipedia.org/wiki/Defensive_wall [Accessed 8 July 2018] Fig. 6.3: Berlin Wall. [online]. Available from: https://www.pinterest.at/pin/415316396866722600/ 90

[Accessed 7 May 2018] Fig. 6.4: Definition of the boundaries of the porosity configuration through a bounding box. Authorâ&#x20AC;&#x2122;s own image Fig. 6.5: Crystal Houses, Amsterdam, MVRDV. [online]. Available from: http://www. talkiesmagazine.nl/news/fashion/chanel-temporary-boutique/ [Accessed 9 July 2018] Fig. 6.6: Detail of Crystal Houses, Amsterdam, MVRDV . [online]. Available from: http://www. talkiesmagazine.nl/news/fashion/chanel-temporary-boutique/ [Accessed 9 July 2018] Fig. 6.7: Glass Farm, Schijndel, MVRDV. [online]. Available from: http://www.abitare.it/en/ architecture/2013/02/27/glass-farm-mvrdv/ [Accessed 9 July 2018] Fig. 6.8: Detail of Glass Farm, Schijndel, MVRDV. [online]. Available from: http://www.abitare.it/ en/architecture/2013/02/27/glass-farm-mvrdv/ [Accessed 9 July 2018]