Mandelbrot

Mandelbrot may refer to Benoit B. Mandelbrot (1924–2010), a Polish-born French-American mathematician who founded the field of fractal geometry and popularized the study of irregular, self-similar shapes. He is best known for introducing the concept of fractals and for the Mandelbrot set, a set of complex numbers c for which the sequence z_{n+1} = z_n^2 + c with z_0 = 0 remains bounded under iteration. The set, visualized through computer graphics, has become a central example in complex dynamics and a symbol of fractal geometry.

Biography: Born in Warsaw to a Jewish family, Mandelbrot spent much of his career in France and the United States. He held faculty and research appointments at several universities and at IBM's research laboratory, and he played a key role in shaping the modern theory of fractals. His 1982 monograph The Fractal Geometry of Nature popularized the subject and influenced science, engineering, and art.

Contributions: Mandelbrot's work established fractal geometry as a mathematical framework for describing natural phenomena that exhibit self-similarity and irregular detail. He explored notions of dimension, scaling, and stochastic processes, and argued that many natural forms cannot be adequately described by traditional Euclidean geometry alone.

Legacy: Fractals have impacted computer graphics, physics, biology, finance, and art, and the Mandelbrot set remains a widely known icon of mathematical visualization.

See also: Mandelbrot set