A formula can be very simple, and create a universe of bottomless complexity.
BENOIT MANDELBROTThink of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
More Benoit Mandelbrot Quotes
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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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Engineering is too important to wait for science.
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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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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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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 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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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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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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Although computer memory is no longer expensive, there’s always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills
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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.
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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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The 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.
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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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An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
BENOIT MANDELBROT