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.
BENOIT MANDELBROTA 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.
More Benoit Mandelbrot Quotes
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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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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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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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Bottomless wonders spring from simple rules, which are repeated without end.
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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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Order doesn’t come by itself.
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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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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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I 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.
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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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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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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 techniques I developed for studying turbulence, like weather, also apply to the stock market
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If you look at a shape like a straight line, what’s remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.
BENOIT MANDELBROT