Benoit Mandelbrot
Benoit Mandelbrot
Benoit B. Mandelbrot was a Polish-born, French and American mathematician with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life." He referred to himself as a "fractalist". He is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal'", as well as developing a theory of "roughness and self-similarity" in nature...
NationalityFrench
ProfessionMathematician
Date of Birth20 November 1924
CountryFrance
Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.
Asking the right questions is as important as answering them
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."
When the weather changes, nobody believes the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed
The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.
Order doesn't come by itself.
A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales.
I was in an industrial laboratory because academia found me unsuitable
If you look at a shape like a straight line, what's remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.
If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
There are very complex shapes which would be the same from close by and far away.
I was asking questions which nobody else had asked before, because nobody else had actually looked at certain structures. Therefore, as I will tell, the advent of the computer, not as a computer but as a drawing machine, was for me a major event in my life. That's why I was motivated to participate in the birth of computer graphics, because for me computer graphics was a way of extending my hand, extending it and being able to draw things which my hand by itself, and the hands of nobody else before, would not have been able to represent.
The existence of these patterns [fractals] challenges us to study 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.