When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
BENOIT MANDELBROTThere are very complex shapes which would be the same from close by and far away.
More Benoit Mandelbrot Quotes
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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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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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An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
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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 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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A fractal is a way of seeing infinity.
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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.
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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.
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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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Order doesn’t come by itself.
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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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A formula can be very simple, and create a universe of bottomless complexity.
BENOIT MANDELBROT