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My book, The Fractal Geometry of Nature, reproduced Hokusai's print of the Great Wave, the famous picture with Mt. Fuji in the background, and also mentioned other unrecognized examples of fractality in art and engineering. Initially, I viewed them as amusing but not essential. But I changed my mind as innumerable readers made me aware of something strange. They made me look around and recognize fractals in the works of artists since time immemorial. I now collect such works. An extraordinary amount of arrogance is present in any claim of having been the first in "inventing" something. It's an arrogance that some enjoy, and others do not. Now I reach beyond arrogance when I proclaim that fractals had been pictured forever but their true role remained unrecognized and waited for me to be uncovered.

 

Benoit Mandelbrot

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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

 

The word fractal, once introduced, had an extraordinary integrating effect upon myself and upon many people around. Initially again it was simply a word to write a book about, but once a word exists one begins to try to define it, even though initially it was simply something very subjective and indicating my field. Now the main property of all fractals, put in very loose terms, is that each part — they're made of parts — each part is like the whole except it is smaller. After having coined this word I sorted my own research over a very long period of time and I realised that I had been doing almost nothing else in my life.

 

Benoit Mandelbrot

 

I do not laugh. I am quite straight-faced as I ask soberly:
"But what on earth is whiteness that one should so desire it?" Then always, somehow, some way, silently but clearly, I am given to understand that whiteness is the ownership of the earth forever and ever, Amen!
Now what is the effect on a man or a nation when it comes passionately to believe such an extraordinary dictum as this? That nations are coming to believe it is manifest daily. Wave on wave, each with increasing virulence, is dashing this new religion of whiteness on the shores of our time. Its first effects are funny: the strut of the Southerner, the arrogance of the Englishman amuck, the whoop of the hoodlum who vicariously leads your mob.

 

W. E. B. DuBois

 

My efforts over the years had been successful to the extent, to take an example, that fractals made many mathematicians learn a lot about physics, biology, and economics. Unfortunately, most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, had been changed by considering the new problems I raised, but largely went their own way.

 

Benoit Mandelbrot

 

I listened while he thought aloud and had almost forgotten my Machiavellian combination, so keen was my relish of the joyous intimacy of this communion with a mind I had passionately loved in his works. He was the first of the great writers of our day whom I had thus approached on something like terms of intimacy. As we talked I observed the strange similarity between his spoken and his written words. I admired the charming simplicity with which he abandoned himself to the pleasures of imagination, his superabundant intelligence, the liveliness of his impressions and his total absence of arrogance and of pose.

 

Paul Bourget