“Think not of what you see, but what it took to produce what you see.”

— Benoit Mandelbrot

“A fractal is a way of seeing infinity.”

“Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.”

“Asking the right questions is as important as answering them.”

“The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.”

“Beautiful, damn hard, increasingly useful. That’s fractals.”

“Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

“Bottomless wonders spring from simple rules, which are repeated without end.”

“The Mandelbrot set is the most complex mathematical object known to mankind.”

“I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.”

“There is a saying that every nice piece of work needs the right person in the right place at the right time.”

“The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.”

“A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales.”

“Being a language, mathematics may be used not only to inform but also, among other things, to seduce.”

“A formula can be very simple, and create a universe of bottomless complexity.”

“When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.”

“Order doesn’t come by itself.”

“An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.”

“In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.”

“Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.”

“I didn’t want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure – I wanted to do something different.”

“I didn’t feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.”

“The most important thing I have done is to combine something esoteric with a practical issue that affects many people.”

“I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.”

“In mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of pages and years and years of learning.”

“If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.”

“Engineering is too important to wait for science.”

“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.”

“I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.”

“The techniques I developed for studying turbulence, like weather, also apply to the stock market.”

“I spent my time very nicely in many ways, but not fully satisfactory. Then I became Professor in France, but realized that I was not – for the job that I should spend my life in.”

“There are very complex shapes which would be the same from close by and far away.”

“Everybody in mathematics had given up for 100 years or 200 years the idea that you could from pictures, from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but then mathematicians had become very abstract.”

“My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.”

“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.”

“Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory.”

“Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.”

“A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don’t get something smooth, but irregularities at a smaller scale.”

“Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics.”

“Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.”

“Although computer memory is no longer expensive, there’s always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills.”

“I don’t seek power and do not run around.”

“Round about the accredited and orderly facts of every science there ever floats a sort of dustcloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to.”

“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.”

“One couldn’t even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn’t expect and expecting to found one would have been pure madness.”

“I was in an industrial laboratory because academia found me unsuitable.”

“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.”

“My fate has been that what I undertook was fully understood only after the fact.”

“There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable.”

“Some mathematicians didn’t even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.”

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