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 MANDELBROTThere is a saying that every nice piece of work needs the right person in the right place at the right time.
More Benoit Mandelbrot Quotes
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Engineering is too important to wait for science.
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The beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn’t expect that it was possible. I just moved from step to step to step.
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When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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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.
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My fate has been that what I undertook was fully understood only after the fact.
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Nobody will deny that there is at least some roughness everywhere
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Bottomless wonders spring from simple rules, which are repeated without end.
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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.
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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.
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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.
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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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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.
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For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
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The Mandelbrot set is the most complex mathematical object known to mankind.
BENOIT MANDELBROT