Mandelbrot Set

[Awani]

[Awani]

[vigilance]

Here's an interesting anecdote regarding Mandelbrot:

'The young Benoit Mandelbrot wanted to become a mathematician. His uncle, Szolem Mandelbrojt, already was one. And he had some sound advice for his nephew. 'Avoid geometry.' The mathematical fashions of his uncle's time placed great value on rigorous analysis and very little on visual imagery. The uncle recommended the young man to study and emulate a piece of mathematical research that capture the approach perfectly, a 300-page article by the French mathematician Gaston Julia on complex analysis - the calculus of v-1. Julia showed that simple mappings of the complex numbers could give rise to monstrously complicated shapes. A rival of Julia's, Pierre Fatou, worked on the same questions at much the same time; and between the two of them they polished off the whole area. At least, so it seemed in the 1940s. Julia and Fatou drew only very crude diagrams of their shapes: Mandelbrot was unimpressed. Like many youngsters before and after him, he ignored the advice of his elders.'

- 'Does God Play Dice: The New Mathematics of Chaos, Ian Stewart.

Also interesting is the comparison of the depiction of Buddha above. I never knew it, but these drawings are actually very carefully mathematical/geometric in nature. Here's a couple of images from "The Tibetan Book of Proportions", which is an 18th century "pattern book", whatever that means: