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Chaos: Making a New Science

Book by James Gleick · 2 quotes · Fractals, Ideas, Mandelbrot

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Chaos: Making a New Science Quotes

“Examined in color through the adjustable window of a computer screen, the Mandelbrot set seems more fractal than fractals, so rich is its complication across scales. A cataloguing of the different images within it or a numerical description of the set's outline would require an infinity of information. But here is a paradox: to send a full description of the set over a transmission line requires just a few dozen characters of code. A terse computer program contains enough information to reproduce the entire set. Those who were first to understand the way the set commingles complexity and simplicity were caught unprepared—even Mandelbrot.”

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“Engineers had not framework for understanding Mandelbrot's description, but mathematicians did. In effect, Mandelbrot was duplicating an abstract construction known as the Cantor set, after the nineteenth-century mathematician Georg Cantor. To make a Cantor set, you start with the interval of numbers from zero to one, represented by a line segment. Then you remove the middle third. That leaves two segments, and you remove the middle third of each (from one-ninth to two-ninths and from seven-ninths to eight-ninths). That leaves four segments, and you remove the middle third of each- and so on to infinity. What remains? A strange "dust" of points, arranged in clusters, infinitely many yet infinitely sparse. Mandelbrot was thinking of transmission errors as a Cantor set arranged in time.”

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Book:Chaos: Making a New Science
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