A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
BENOIT MANDELBROTThe theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient.
More Benoit Mandelbrot Quotes
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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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Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.
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A formula can be very simple, and create a universe of bottomless complexity.
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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 didn’t want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure – I wanted to do something different.
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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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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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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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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
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The Mandelbrot set is the most complex mathematical object known to mankind.
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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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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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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.
BENOIT MANDELBROT