D’Arcy Wentworth Thompson was among the first to cross the frontier between mathematics and the biological world and as such became the first true biomathematician. His main work is the book “On Growth and Form” (published in 1917, expanded version  published in 1942).

In the last chapter “On the Theory of Transformations , or the Comparison of Related Forms”, the author shows how differences between organisms can be presented geometrically. He saw form as a mathematical problem and growth as a physical problem.

Thompson was inspired by Albrecht Dürer’s works who used grid systems in his studies of human proportion. (Geometry, Treatise on Proportion). These works influenced Thompson’s theory of coordinates, which stated that the process of evolution as well as development could be comprehended mathematically by applying certain topological transformations.

An important topic discussed is how he regarded the mathematical transformation. He believed that all mathematical points that comprised a line drawing respected the principle that biological homology pertained to structures, but not necessarily individual point locations on structures. Rather, it was how the mathematical points were represented as a whole. His diagrammatic representation consisted of a superimposed grid that he used to to judge whether he had developed a reasonable formula for a specific form transformation. Clearly the only purpose of the mathematical grid was to demonstrate the whole geometry of the transformation as a deformed coordinate system.

In his transformational grids he used the principle of plot points where each point corresponded to another and are defined in the space which is the basis of parametric design. This book is still relevant nowadays to understand the process and evolution of transformation. What should be considered here is that the transformation is not random but due to a certain mathematical logic.

Doubts

1. What if something is already deformed – how can you explain it mathematically?

2. Thompson only analyzed parts of organisms as opposed to creating a thorough analysis on the whole thing.

3. Thompson doesn’t explain relation to function but explains the jump in progress of forms while the evolution explains functionality.

Thompson viewed organic form as a ‘diagram of forces’ from which we can infer that the nature of the forces that act upon it now can be the same forces that have acted upon it in the past. With the help of this force metaphor, He saw how these different forces changed during both ontogenetic and evolutionary history. He concluded this through the mathematical comparison of forms.

Currently the technology that we us to produce architecture is evolving at a rapid pace, therefore I am interested in how the current technology responds to nature. There have been many examples of how architecture mimics the natural environment. With the aid of parametric technology, forms can be manipulated and transformed to resemble almost anything. I propose to research how we can manipulate parametric forms that can adapt to a certain environment as nature adapts to its particular environment.