Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.
BENOIT MANDELBROTIf 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.
More Benoit Mandelbrot Quotes
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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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I don’t seek power and do not run around
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A fractal is a way of seeing infinity.
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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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Think not of what you see, but what it took to produce what you see.
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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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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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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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There is a saying that every nice piece of work needs the right person in the right place at the right time.
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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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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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Order doesn’t come by itself.
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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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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.
BENOIT MANDELBROT