A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
BENOIT MANDELBROTI 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.
More Benoit Mandelbrot Quotes
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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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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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Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
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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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There are very complex shapes which would be the same from close by and far away.
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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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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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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 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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Bottomless wonders spring from simple rules, which are repeated without end.
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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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My fate has been that what I undertook was fully understood only after the fact.
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There is a saying that every nice piece of work needs the right person in the right place at the right time.
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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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The most complex object in mathematics, the Mandelbrot Set … is so complex as to be uncontrollable by mankind and describable as ‘chaos’.
BENOIT MANDELBROT