A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales...
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As quoted in a review of The Fractal Geometry of Nature by J. W. Cannon in The American Mathematical Monthly, Vol. 91, No. 9 (November 1984), p. 594Benoit Mandelbrot
» Benoit Mandelbrot - all quotes »
I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.
Benoit Mandelbrot
Do I claim that everything that is not smooth is fractal? That fractals suffice to solve every problem of science? Not in the least. What I'm asserting very strongly is that, when some real thing is found to be un-smooth, the next mathematical model to try is fractal or multi-fractal. A complicated phenomenon need not be fractal, but finding that a phenomenon is "not even fractal" is bad news, because so far nobody has invested anywhere near my effort in identifying and creating new techniques valid beyond fractals. Since roughness is everywhere, fractals — although they do not apply to everything — are present everywhere. And very often the same techniques apply in areas that, by every other account except geometric structure, are separate.
Benoit Mandelbrot
I feel that we are living a very fragmented life; the whole world — you too. So I perceive the world in fragments. It is somewhat like being on a very fast train and getting glimpses of things in strange scales as you pass by. A person can be very, very tiny. And a billboard can make a person very large. You see the corner of a house or you see a bird fly by, and it's all fragmented. Somehow, in painting I try to make some logic out of the world that has been given to me in chaos. I have a very pretentious idea that I want to make life, I want to make sense out of it. The fact that I am doomed to failure — that doesn't deter me in the least.
Grace Hartigan
Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.
David Deutsch
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."
Benoit Mandelbrot
Mandelbrot, Benoit
Mandelson, Peter
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