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 MANDELBROTA formula can be very simple, and create a universe of bottomless complexity.
More Benoit Mandelbrot Quotes
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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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Nobody will deny that there is at least some roughness everywhere
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Asking the right questions is as important as answering them
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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Engineering is too important to wait for science.
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A fractal is a way of seeing infinity.
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Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.
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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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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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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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Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
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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 Mandelbrot set is the most complex mathematical object known to mankind.
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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
BENOIT MANDELBROT