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.
BENOIT MANDELBROTBoth 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.
More Benoit Mandelbrot Quotes
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Beautiful, damn hard, increasingly useful. That’s fractals.
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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.
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In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.
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I had very, very little training in taking an exam to determine a scientist’s life in France.
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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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I had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening.
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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.
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I was in an industrial laboratory because academia found me unsuitable
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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I’ve been a professor of mathematics at Harvard and at Yale. At Yale for a long time. But I’m not a mathematician only. I’m a professor of physics, of economics, a long list. Each element of this list is normal. The combination of these elements is very rare at best.
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Think not of what you see, but what it took to produce what you see.
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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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Bottomless wonders spring from simple rules, which are repeated without end.
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I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
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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.
BENOIT MANDELBROT