Benoit Mandelbrot
26.10.2010 07:32 | mensch | cklem
Der Entdecker der Fraktale, Benoit Mandelbrot, starb am 14. Oktober.


a bird, Donnerstag, 9. Dezember 2010, 11:10
That is very interesting. I would like to see one of those artificial shapes being phisicaly build rather than just a result of a computer program.
But then again, isn't a simple square a 'man made' shape?
Or where do you get squares in nature?

cklem, Freitag, 10. Dezember 2010, 07:00
on one hand you're absolutely right: there are no things in nature that correspond exactly to a mathematical object (even when only concerning their shape). but what the concept of fractals achieved is, that the zoo of geometrical objects was extended to forms that approach many natural shapes better. this is due to the property of self-similarity, like illustrated by the example of the curliflower at the beginning of the talk. there are also computer models, that generate shapes more natural like this picture. it was generated by a fractal growth model (FGM). such models are based on the understanding that self-similarity in nature is caused by repeated growing steps, while in mathematics it is realized by repeated iteration steps. this picture does not look so "man made" because in FGMs each iteration step gets some small randomly perturbation added, which makes the shape more "blurry" and simluates the fact that in nature, each growth step follows the same rule, but the environment is different each time.

in this article i illustrate one way of generating fractals (even if it is not about such "natural" ones).