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 MANDELBROTA fractal is a way of seeing infinity.
More Benoit Mandelbrot Quotes
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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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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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Order doesn’t come by itself.
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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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If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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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There are very complex shapes which would be the same from close by and far away.
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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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For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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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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A formula can be very simple, and create a universe of bottomless complexity.
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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
BENOIT MANDELBROT