Moreover, one of the most currently fascinating mathematical theories is no doubt the theory of fractals: according to the definition of its recently passed away discoverer, the polish mathematician Benoit Mandelbrot (1975), who started his researched form the fractal structure found out by french mathematicia Gaston Julia in 1920, fractals are geometrical figures characterized by a repetition to infinity of a same pattern on a more and more reduced scale. Nature is in fact filled with forms very similar to fractals, which don't follow in any way any of the rules of Euclidean geometry. A coastline, the branches or the roots of a tree, a cloud, the snowflakes, the zigzag lightning bolts and the leaf venation patterns: these are only a few examples of fractal forms spontaneously creating in nature.
Among these ones there is the spiral, the fractal form par excellence. The procedural, generative, hieratic and evolutionary element can therefore be considered the key of this thought, turned to a modern "computational ecology": almost 40 years of study, analysis and research have passed between Alan Turing's revolutionary theories about morphogenesis (the capability of every living being to develop complex bodies starting from very simple elements, using self-assembling processes without an external guide), which followed those by bio-mathematician Thompson D'Arcy in his work 'On the Growth and Form' (1917), and more recent studies (1980-1985) on genetic algorithms (a particular kind of evolutionary algorithms utilizing mutation, selection and other recombination techniques in order to guarantee a certain number of abstract representations of possible solution for optimization to become better solutions). Those researches were meant to point out the almost computational characteristics of Mother Nature on one hand, while on the other they confirmed the analog/digital machines' capability of simulating and replicating complex natural phenomena.