A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
BENOIT MANDELBROTNobody will deny that there is at least some roughness everywhere
More Benoit Mandelbrot Quotes
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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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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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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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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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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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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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A fractal is a way of seeing infinity.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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.
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The Mandelbrot set is the most complex mathematical object known to mankind.
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Engineering is too important to wait for science.
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If one takes the kinds of risks which I took, which are colossal, but taking risks, I was rewarded by being able to contribute in a very substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems.
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There are very complex shapes which would be the same from close by and far away.
BENOIT MANDELBROT