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.
BENOIT MANDELBROTA fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
More Benoit Mandelbrot Quotes
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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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Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
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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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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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I 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.
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Nobody will deny that there is at least some roughness everywhere
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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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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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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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Asking the right questions is as important as answering them
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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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Think not of what you see, but what it took to produce what you see.
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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.
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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.
BENOIT MANDELBROT