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.
BENOIT MANDELBROTIf you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
More Benoit Mandelbrot Quotes
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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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My fate has been that what I undertook was fully understood only after the fact.
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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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There are very complex shapes which would be the same from close by and far away.
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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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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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I’ve been a professor of mathematics at Harvard and at Yale. At Yale for a long time. But I’m not a mathematician only. I’m a professor of physics, of economics, a long list. Each element of this list is normal. The combination of these elements is very rare at best.
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A formula can be very simple, and create a universe of bottomless complexity.
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Order doesn’t come by itself.
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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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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
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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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Bottomless wonders spring from simple rules, which are repeated without end.
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The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.
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Beautiful, damn hard, increasingly useful. That’s fractals.
BENOIT MANDELBROT