A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
BENOIT MANDELBROTBottomless wonders spring from simple rules, which are repeated without end.
More Benoit Mandelbrot Quotes
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Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.
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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.
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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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A formula can be very simple, and create a universe of bottomless complexity.
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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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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.
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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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I had very, very little training in taking an exam to determine a scientist’s life in France.
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A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don’t get something smooth, but irregularities at a smaller scale.
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The beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn’t expect that it was possible. I just moved from step to step to step.
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I don’t seek power and do not run around
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My fate has been that what I undertook was fully understood only after the fact.
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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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Order doesn’t come by itself.
BENOIT MANDELBROT