3. NATURAL CONSTRUCTIONS INFORMING ARCHITECTURE
3.3. Biological Constructions and Closest Packing
itself (…)”48. It is attributed to a quality of all living systems to reproduce by themselves. Moreover, they exert an unexpected behaviour and a complex, non-linear way of dynamic growth and adaptation in space (dynamical systems). They are composed of many parts and try to preserve their thermodynamic equilibrium through the transformation of energy (food chain49) or through the exchange of energy with other neighbour organisms. At the same time, they adapt to environmental changes and try maintaining themselves by making genetic changes in the attributes of their following generations50. Briefly, the autopoietic organisation is considered to be a unified network of generative parts that act recursively in this system and consider them as a unit in space, through which they exist. In living organisms, this generative organisation is the autopoietic organisation51.
3.3. Biological Constructions and Closest Packing
also necessary to uncover the structure that those systems consist of.
Examining nature’s biological constructions, numerous naturally developed substances and systems are observed, whether these may refer to organic or inorganic, animate or inanimate matter, generated by closest packing or ‘tessellation’. Closest packing is a very common chemical or structural arrangement found in nature, constituting several materials and biological systems and proves to be the result of nature’s tendency to self-obtain stability in its systemic organisation.
(self-organisation)
Microstructures such as those of the bone’s inner structural arrangement presented previously and almost the majority of the materials’ microstructures that are self-assembling their inner condition are included within a category called “cellular solids”. The term derives from the Latin “cella” (small compartment) and by the Roman “cellarium’ that implies a cluster of cells. They are made up of an interconnected network of solid struts or plates, which create the edges and faces of cells. There are three distinct types: The first and
Figure 10: Example of open-celled foams (left) and closed-cell foams (right)
the simplest one is the two-dimensional array of polygons, which pack to fill a plane area resembling the hexagonal cells of the bee, and thus it is called honeycomb (Figure 11). Moreover, they can be commonly found as a packed three-dimensional array of polyhedral that fill a space, and these three-dimensional cellular solids are called foams. If the foams are connected together with cell edges, so that the faces are open, then they are called open-celled foams. Alternatively, if the cells are connected together with solid cell faces, they are then called closed-celled foams. Certainly, they exist in combinations of both open-celled and closed-celled foams (Figure 10).
Their emergent structure has fascinated several philosophers, mathematicians, and scientists for over 300 years. Hook was the first who attempted to observe them, while later Lord Kalvin tried to analyse them. In addition, Charles Darwin and D’Arcy Thompson attempted to understand their origin and function. There are several characteristics that can influence their properties and structure. The most important
Figure 11: Honeycomb is the simplest form of a two-dimensional cellular solid. The analysis conducted on the honeycomb geometry revealed that the hexagonal subdivision is the most efficient/optimum way of partitioning a two-dimensional space, in terms of requiring the minimum amount of beeswax material to create the whole honeycomb surface.
one is their relative density p*/ps (the density of p* of the foam is divided by that of the solid of which is made of ps), while the remaining pore space is called porosity and can be obtained by this equation 1- p*/ps. Other parameters are the cell shape and cell size and cell connectivity, but having less effect on the overall material performance.
Nevertheless, their structure varies from a very ordered, such as the hexagonal honeycomb, to absolute disordered, like the three- dimensional sponge networks.
The remarkable thing about those natural subdivisions is that they also manage to be energy efficient, an intriguing element that moved mathematical and computational investigations towards such natural geometries. The analysis conducted on the honeycomb geometry revealed that the hexagonal subdivision is the most efficient/optimum way of partitioning a two-dimensional space, in terms of requiring the minimum amount of beeswax material to create the whole honeycomb surface, while being rigid and stable also. However, in the case of three-dimensional space Lord Kelvin conjecture52, a convex uniform honeycomb created by the truncated octahedron, which is a 14-faced space-filling polyhedron (a tetrakaidecahedron), with 6 square faces and 8 hexagonal faces (Figure 12). However, recent advances with the aid of computer software and computation have pointed another mathematical discovery, based on the dry foam bubbles. The Weaire-Phelan foam structure is constituted from six (6) 14-sided (12 pentagonal and 2 hexagonal, the tetrakaidecahedron)
52 https://en.wikipedia.org/wiki/Weaire%E2%80%93Phelan_structure, Accessed: 22/01/2016
and two (2) 12sided combination of polyhedrons and have managed to reduce Lord Kelvin’s proposal by almost 0.3%. In chemistry, it can be observed as a crystal structure where it is usually known as the
"Type I clathrate structure".
There are various types of natural foam structures. Unlike the man-made foams that display more regularity in their cell size dispersion using shapes such as the triangle, the square, and hexagon, natural foams are presenting greater variation in their cell size and distribution. Some materials have closed-celled foams, such as balsa or cork, others such as bone tissue (mentioned earlier) and sponge structures are open-celled, presenting a connectivity of four, five or even six cells (Figure 10, Figure 11). Nevertheless, there are still some more that their cells are assembled in such organisation or in a
Figure 12: Kelvin’s conjecture, tetradecahedra, believed to be the most efficient way of partitioning a three-dimensional space.
specific direction with properties that are measured according to that direction. 53
Generally, all natural and biological constructions demonstrate a disperse distribution in their porosity and cell size, so broad that the largest cells are hundreds of times bigger than the smallest. Dispersion here does not only imply anisotropy but rather both of them are related to the overall creation of these natural materials. Nevertheless, the way that the foam cells are randomly distributed and linearly grown has influenced mathematical and computational discoveries presented in the following Chapters.
53 Gibson, Lorna J., (1997), pp. 15-49.
Figure 13: Cork microstructure (left) and iris leaf structure (right), examples of closed-celled foams, (Gibson, Lorna J., 1997)
Conclusively, those philosophical ideas about form and structure and a proposed reversed model of bottom-up design approach, the material and biological models have become interesting paradigms for advanced architectural design in computational architecture. Whilst they have informed several mathematical discoveries, inspired digital techniques and can become the basis for physical investigations and digital simulations for new morphogenetic models in architecture. Moreover, this ability of material systems to adapt to severe stress conditions and self-organize into a more stable organisational system can re-generate design strategies that have the capacity to respond to the changing built environment and be optimised accordingly, such as optimisation procedures and genetic algorithms. When referring to architectural form and materiality, those concepts of adaptation and self-organisation are transforming their external reference factor to a building’s conditional system. Loading
Figure 14: Natural sponge microstructure (open-celled foam example).
conditions, such as gravity, wind, lateral, and live loads, thermal and earthquake loads shall be taking place, whilst the way that material, form and structure are organised becomes important too.