My fate has been that what I undertook was fully understood only after the fact.
BENOIT MANDELBROTI 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.
More Benoit Mandelbrot Quotes
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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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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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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 was in an industrial laboratory because academia found me unsuitable
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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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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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When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
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I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
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Beautiful, damn hard, increasingly useful. That’s fractals.
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Nobody will deny that there is at least some roughness everywhere
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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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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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Unfortunately, the world has not been designed for the convenience of mathematicians.
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A formula can be very simple, and create a universe of bottomless complexity.
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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.
BENOIT MANDELBROT