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Mandelbrot fractal video9/25/2023 ![]() One begins by assigning a fixed value to c, letting z = 0 and calculating the output. The terms z and c are complex numbers, which consist of an imaginary number (a multiple of the square root of –1) combined with a real number. Part of the charm of the set is that it springs from such a simple equation: z 2 + c. "It is really quite fundamental," he says. Sullivan of the City University of New York calls it a "crucible" for testing ideas about the behavior of dynamical (or nonlinear, or complex, or chaotic) systems. Even those who scorn the set's popularity acknowledge its mathematical significance. ![]() Devaney of Boston University, who says he admires Mandelbrot's work, "there would be no controversy." "Were it not for his personality," remarks Robert L. Mathematicians are not known for priority battles, but Mandelbrot-a self-described "black sheep "-has often bumped heads with colleagues. These assertions have long circulated in the mathematics community but have only recently surfaced in print. A third asserts that his work on the set not only predated Mandelbrot's efforts but also helped to guide them. ![]() Two maintain that they independently discovered and described the set at about the same time as Mandelbrot did. Three other mathematicians have challenged his claim. He refers to its image as his "signature." Mandelbrot claims that he and he alone discovered the Mandelbrot set-which has fractal properties-about a decade ago. He is best known for coining the term fractal to describe phenomena (such as coastlines, snowflakes, mountains and trees) whose patterns repeat themselves at smaller and smaller scales. Mandelbrot, a mathematician at the IBM Thomas J. ![]() The infinitely intricate computer-generated image of the set serves as an icon for the burgeoning field of chaos theory and has attracted enormous public attention. The set has been called (in this magazine) "the most complex object in mathematics." That is debatable, yet it is almost certainly the most famous such object. Who discovered the Mandelbrot set? This is not a trick question-or a trivial one. The phrasing of some references to dates has been changed, in brackets, for clarity. Editor's note: This article originally appeared in the April 1990 issue of Scientific American, under the title "Mandelbrot Set-To." We are posting it now to coincide with our reporting on a talk this week by Benoit Mandelbrot at Columbia University on fractals and financial markets. ![]()
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