(Bassil Taleb, Sequential Transformation)

### ”On the Theory of Transformations” (“On Growth and Form” , 1917)

D’Arcy Wentworth Thompson wrote his book in the beginning  of XX century, in 1917. He was one of the first scientists that explored the connection, and tried to blur the boundaries between biology and mathematics. Large part of “On Growth and Form” is devoted to transformations of biological shapes and forms viewed  as mathematical and physical methods. This chapter is highlighting mathematical descriptions of  how physical processes affect biological changes. Thompson uses grid systems and presents us his theory of coordinates. This theory expresses that transforming the grid we can see  a mathematical logic in the evolution and biological growth. Thompson gave a lot of examples of forms represented nature: bones, leaves, skulls and so on,  and explanations  of changing shapes of one species according mathematical system of coordinate. Some images he used was taken from the artist and mathematician Albrecht Dürer’s work on proportion: “De Symmetria Partium in Rectus Femoris Humanorum Corporum Libri”.   D’Arcy Wentworth Thompson uses four basic types of deformation of the Cartesian grid of coordinates to learn the development of the biological shapes:

1. Linear variations along XY axis (fish eye resembles human eye after that kind of transformation)
2. Non-linear transformation which is based on logarythmic definitions
3. Shear concept – usage of various angles to transform
4. Radial transformation – in which one set of lines are represented as radiating from a focal point, while the other set is transformed into circular arcs cutting the radii orthogonally.
By comparing bones, leaves, skulls etc. Thompson shows us the organic shapes and forms as a diagram that explains mathematically the history of the evolution.
It is interesting how nowadays this knowledge and the study of  biological transformations in general can be related and connected to new technology, digital tools. there are a lot of examples how architectural forms imitate the nature. I think it could be interesting to research about how nature adapts to its surroundings, so that we could understand how to create and manipulate parametrical forms connecting them to a certain environment.