Mandelbrot Quotes

“Consider cotton prices," Malcolm said. "There are good records of cotton prices going back more than a hundred years. When you study fluctuations in cotton prices, you find that the graph of price fluctuations in the course of a day looks basically like the graph for a week, which looks basically like the graph for a year, or for ten years. And that's how things are. A day is like a whole life. You start out doing one thing, but end up doing something else, plan to run an errand, but never get there... And at the end of your life, your whole existence has that same haphazard quality, too. Your whole life has the same shape as a single day.”
― Michael Crichton, Jurassic Park

“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.”
― James Gleick, Chaos: Making a New Science

“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.”
― James Gleick, Chaos: Making a New Science