Amorphous Morphology

"I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid - a term used in this work to denote all of standard geometry - Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being 'formless,' to investigate the morphology of the 'amorphous.' Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel."

- Benoit Mandelbrot (1924 - 2010)
The Fractal Geometry of Nature

Catalytic Geometry

"Why is geometry often described as 'cold' and 'dry?' One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line... Nature exhibits not simply a higher degree but an altogether different level of complexity." - Benoit Mandelbrot, The Fractal Geometry of Nature

"Life emerged, I suggest, not simple, but complex and whole, and has remained complex and whole ever since—not because of a mysterious élan vital, but thanks to the simple, profound transformation of dead molecules into an organization by which each molecule's formation is catalyzed by some other molecule in the organization. The secret of life, the wellspring of reproduction, is not to be found in the beauty of Watson-Crick pairing, but in the achievement of collective catalytic closure. So, in another sense, life—complex, whole, emergent —is simple after all, a natural outgrowth of the world in which we live." - Stuart Kauffman, At Home in the Universe