In this investigation we tried to learn D’arcy Thompson’s theory on growth and form and apply it to architecture. So we figure out that it could be a new approach in creating architecture not from divided parts but growth it like live organism. We also explored this dynamic processes through prism of Grasshopper tools.
Here you can see our presentation video

T1 Watercube -Digital Logics-Critical Analyze

T1 Thompson D. On growth and form-Readings

Both text related to the search forms in nature with subsequent implementation them into architecture.But because in the architecture we possess a much smaller set of tools than is in the arsenal of nature, a simple copying of the original natural forms is excluded and therefore we are obliged to comprehend the laws themselves of formation of these shapes and translate them into common concepts of modern mathematics and geometry, It is difficult, but very exciting way .
D’arcy Thompson was an outstanding Scottish biologist and mathematician and pioneer in the theory of transformation. In his writings, He is based on such theories as the topology of Henri Poincaré, the coordinate system theory of Descartes and Aristotle’s theory of species.

There are two ways of studying forms – descriptive and analytical, descriptive is good for the first step, but it is not versatile, what cannot be said about the analytical, which is seemed inflexible enough for everyday use at first glance , but its rigidity combines with infinite freedom.After all, the laws of geometry and mathematics are valid anywhere in the world, so the exact definition of geometric figures relate to all figures of this type, but how diverse they may be!Analytical approach provides the perfect universal descriptive system that can predict a lot of changes in transformation of a particular type. We find homologies and similarities that were not obvious to us earlier, for example, we learn that no matter how we keep the chain and threw the stone, the resulting loop circuit or path of the stone always mathematically homologous.Moreover, this method helps to understand not only the static form, but a dynamic process, as well as forces that create this process. The understanding of the magnitude and direction of forces is fundamental in the study of the transformation of related forms. Although a mathematical approach is still not perfect and still are many mathematical processes hidden from us, humanity has reached enormous advances in understanding the mathematical nature of the world.

Sir D’arcy Thompson had based on Descartes’ coordinate system in his study of the transformation of species. The method consists in the fact that using the normal orthogonal or radial grid you can see an incredible variety of modifications occurring in nature.Thus, when applying a simple two-dimensional contour of fish or plant leaves, or skull, or bones on the grid, and the subsequent transformation of the grid using the offset coordinate rotation axes and other manipulations literally before our eyes miracle of evolution happens for which Nature spent more than one million years. So after the compression or stretching or turning the mesh the contour of the object deforms as well and relatively distant in appearance bones of bull and giraffe acquire the obvious connection.

D’arcy Thompson’s method is also notable for the fact that he treats the subject in the unity of its properties and characteristics, while zoologists and botanists first try to divide and consider all alone, so to speak fin separately and fish individually, this approach leads to a complication system and ultimately to its fully non-obviousness.

As for my personal views on this research question, I would be interested to continue this research, but to use a three-dimensional model for the transformation, as well as to find common ground with the theory of Poincare’s undivided authority and transformation of all things in the world. It seems to me that this issue has deep philosophical roots and comprehend the theory of transformation, we begin to understand better the nature of this world, how, why and what for we and all in this world have been created.

Thompson wrote On Growth and form in the maturity of a career that lay somewhat outside the mainstream of the biological sciences of his day. His writings were a large contribution for the study of morphology. On Growth and Form is essentially an attempt to establish a concept of organic form based upon the physical and mathematical laws governing the development and function of organisms. He demonstrates in this chapter that how organic forms once put in a Cartesian grid can change forms in the same species and how this method could be used to find missing parts in the series of relative species

During the debate in the class we found the book is more of a concept and basically starts with the theory of transformation and is solidly based upon the laws of Newtonian Physics. All the experiments D’Arcy conducted were in 2D and not in 3D and gives a mathematical approach to the biological forms. He tries to show how the relationship between similar species is still there but changing their coordinates and the position of the parts changes. It’s a form finding method found over 100 years ago and gives us an idea of multiplicity during that era. Topology has been explained as a concept here with no real results. It’s a relation of a part to a whole.

The Next part of the critical analysis was The Water Cube-Beijing National Aquatics Centre by ARUP. The structure is made up of the soap bubbles which symbolise the square in the Chinese culture. The beautiful geometry is based on Weaire Phalen foam structure with an array of soap bubbles where 75% of the cells have 14 faces and the other 12 faces. In spite of the complete regularity, the structure when viewed at different angle looks completely random and organic. The polyhedron structure works perfectly as an extremely energy efficient and possibly the most earthquake resistant building. The water cube is a steel space frame structure with 4000 ETFE bubbles, the material being 8 times thinner than even a penny, which are pumped in with a low pressure. The building captures 20% of the incident solar energy and requires 90% less potable water than an equivalent building and uses 55% less artificial lighting. The ETFE IS 1% of glass weight and acts as a thermal insulator. The whole structure weighs almost as much as the Eiffel tower.

Research line:

After reading On growth and form, I’m interested in studying and researching more about Topology in Architecture. Architectural topology is a mutation of form, structure, context and interwoven patterns and dynamic complexity in space. Topological space differs from Cartesian space within which it forms different forms. It’s a process of continuous deformation. There are differentiable dynamic systems in architecture like chaos theory and fractal geometry. Would like to research on the role of topology in architecture and which structure/buildings it can be applied to.

Image reference-http://futuresplus.net/tag/topology/