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.
BENOIT MANDELBROTI was in an industrial laboratory because academia found me unsuitable
More Benoit Mandelbrot Quotes
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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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The most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.
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It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.
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The Mandelbrot set is the most complex mathematical object known to mankind.
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The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.
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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 my time very nicely in many ways, but not fully satisfactory. Then I became Professor in France, but realized that I was not – for the job that I should spend my life in.
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The techniques I developed for studying turbulence, like weather, also apply to the stock market
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My fate has been that what I undertook was fully understood only after the fact.
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Round about the accredited and orderly facts of every science there ever floats a sort of dustcloud of exceptional observations, of occurrences minute and irregular and seldom met with, which it always proves more easy to ignore than to attend to.
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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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A formula can be very simple, and create a universe of bottomless complexity.
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Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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Asking the right questions is as important as answering them
BENOIT MANDELBROT