Engineering is too important to wait for science.
BENOIT MANDELBROTI went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
More Benoit Mandelbrot Quotes
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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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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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Nobody will deny that there is at least some roughness everywhere
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My fate has been that what I undertook was fully understood only after the fact.
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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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Bottomless wonders spring from simple rules, which are repeated without end.
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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 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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Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
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Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.
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A formula can be very simple, and create a universe of bottomless complexity.
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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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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.
BENOIT MANDELBROT