The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel … - Benoit Mandelbrot

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."

The Mandelbrot set is the modern development of a theory developed independently in 1918 by Gaston Julia and Pierre Fatou. Julia wrote an enormous book — several hundred pages long — and was very hostile to his rival Fatou. That killed the subject for 60 years because nobody had a clue how to go beyond them. My uncle didn't know either, but he said it was the most beautiful problem imaginable and that it was a shame to neglect it. He insisted that it was important to learn Julia's work and he pushed me hard to understand how equations behave when you iterate them rather than solve them. At first, I couldn't find anything to say. But later, I decided a computer could take over where Julia had stopped 60 years previously.

Unfortunately, the world has not been designed for the convenience of mathematicians.