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.
BENOIT MANDELBROTI spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.
More Benoit Mandelbrot Quotes
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Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.
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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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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 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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One couldn’t even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn’t expect and expecting to found one would have been pure madness.
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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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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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Asking the right questions is as important as answering them
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Think not of what you see, but what it took to produce what you see.
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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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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 beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn’t expect that it was possible. I just moved from step to step to step.
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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