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

Concept – Transformation, growth, forces and deformation

Architectural work- Embryological House by Greg Lynn

Click the link below for the video of the final presentation:

Case study:    Watercube_Beijing National Aquatics Center_ PTW Architects, CSCEC, CCDI,  Arup

Reading:   On Growth and form_ D’Arcy Wentworth Thompson

Nature and the notion of organic have always been of much interest from architects designers and urban planners. Extensive theoretical studies, as well as architectural applications, have attempted to simulate nature, by extracting forms, geometries and principles found in living organisms.

The Beijing National Aquatics Center designed by  PTW Architects, CSCEC, CCDI, and Arup is one of the most recent examples of applying natural systems in architectural design processes. In this building, vastly known as the Watercube, the strict geometry found in water bubbles was used as an inspiration for the exterior of the building, forming an iridescent cellular façade that diffuses natural light. The continuous skin, made by the ETFE material, was created as a steel structure housed in a cavity, filled by platonic solid units, that seem to be completely random, but in reality are different units that are repeated to the whole exterior of the building. The algorithmic relations that form the façade and roof of the Watercube, as well as the multiplicity of their units have been subject to great debate about the application of parametricism  in architectural and urban design context.

The former principles of natural forms were long before theoretically analyzed from  D’Arcy Wentworth Thompson in his book On Growth and form, almost a century ago. In his book, and particularly in the chapter On the Theory of Transformation, Or the Comparison of Related Forms, D’Arcy sets the basis of parametric design, at a conceptual level, through analyzing and comparing natural forms using mathematical justifications. The author explored the interrelations of growth, form and physical forces found in different relative species and the topological similarity of family variations, through grid and co-axial transformations and stretching of the natural geometries and structures of living organisms (leaves, fishes, animals, etc.). Though this study was carried out in a two dimensional level, it is implied that it can be extended into a three dimensional one, extrapolating important relations and principles between relative species, through breaking down the geometries at fractal basis. The notion of topology as a concept, that is evident in D’Arcy;s study, establishes a contemporary parametric design approach in a conceptual level.

As a future research, I would be highly interested in researching and comparing the new digital logics that are found in the recent parametric architectural examples, as well as exploring the relations that form them in a three dimensional level.

Image source: http://www.l-a-v-a.net/projects/beijing-watercube/

In Thomson’s book “On Growth and Form”, he looks at the way natural living things, such as vegetation and animals, and why they take the form they do by growing and changing. While at first the forms are described with words, they later are represented with mathematical and graphical drawings. Thomson admits that the mathematical analysis has its limitations since one cannot simply draw anything. However, it does have an advantage in a way we can manipulate shapes and discover new things; he places a grid and then deforms it consistently in one particular pattern, the result is a new species. Nevertheless not everything can be transformed to anything; a vertebral animal cannot be transformed to a mammal. His study of form is called “morphology”. The form goes from a static to dynamic state with the influence of forces on them. While looking at the shape we can recognize the force that transformed it, which can be for example Gravity. By understanding the form transformation vs. the forces, we can see a similarity with DeLanda in the evolution process from young to older. Thomson discuses the concept of average since the process of transformation allows you to get only an approximate result; one can get mathematical forms for shapes in general, but not for a specific case – “Keep the type in mind & leave the single cases, with all its accidents, alone”. In “On Growth and Form”, there is also the idea of Newton which says that “Nature delights in transformation”. The book is mostly about questioning and comparing the form, growth and Cartesian coordinates. According to Thomson, comparison of related forms allows us to understand better the transformation and deformation that if we saw the form alone. His method was to use Cartesian coordinates, and it can be used to study missing parts of an animal or the missing steps of the evolution process. Thomson describes Listing’s point of view of seeing a topological similarity in mammals where in the science of typology any form can be changed to any form. This concept comes behind the fact that if you breakdown different forms, we will end up with similar basic geometric shapes. However Thomson did not study this perspective. All of his experiments are limited since they are in 2D, where everything in the grid changes but keeps the same relation. His study can be applied on a 3D grid but there will be difficulty in correlating one plane into different one. Moreover, even in his 2D process, we can notice that his transformation from the initial drawing to the obtained result is not always very accurate and sometimes raises doubts about certain coordinate’s displacement; Nevertheless we should keep in mind the book was written in a time where computer analysis and parametric still did not exist, making his work an impressing read. We can notice that Thomson applied the same method as Albert Durer did on human face, but for animals.

In my personal research, I would like to experiment and apply Thomson’s theories since he was descriptive rather than experimental in his book. It is clear that he was aware of that when he said: “This book of mine has little need of preface, for indeed it is ‘all preface’ from beginning to end”. It would be to apply the study to all shapes in our daily life to follow their process and see what forces and changes they have been affected by to become transformed to what they are.

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/