There are very complex shapes which would be the same from close by and far away.
BENOIT MANDELBROTI was in an industrial laboratory because academia found me unsuitable
More Benoit Mandelbrot Quotes
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Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
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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.
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Think not of what you see, but what it took to produce what you see.
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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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Unfortunately, the world has not been designed for the convenience of mathematicians.
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If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
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A fractal is a way of seeing infinity.
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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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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
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Nobody will deny that there is at least some roughness everywhere
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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Bottomless wonders spring from simple rules, which are repeated without end.
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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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The Mandelbrot set is the most complex mathematical object known to mankind.
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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 MANDELBROT