The story
Benoit Mandelbrot, a Polish-born mathematician working at IBM in New York, introduced the word fractal in 1975 in a French book, Les objets fractals, taking it from the Latin fractus, meaning broken. A fractal is a shape that stays rough at every magnification, and whose dimension can be fractional. In a 1967 paper, How Long Is the Coast of Britain?, he had shown that a coastline's measured length keeps growing as the ruler shrinks, an idea he took from the English scientist Lewis Fry Richardson. His books of 1977 and 1982, the latter titled The Fractal Geometry of Nature, brought the idea to a wide audience, and in 1980 IBM computers first plotted the shape now called the Mandelbrot set.
Nineteenth century mathematicians had met such shapes, among them the Cantor set and the Koch snowflake, and treated them as curious monsters. Edward Lorenz's chaos theory of 1963 showed that simple rules can produce endlessly intricate behavior, and the strange attractors of chaotic systems turned out to be fractal. Mandelbrot named the family, tied it to measurable quantities, and used computer pictures to make it convincing. Fractal methods now appear in computer graphics, the study of branching in lungs and blood vessels, and models of financial markets, where he argued price changes are far wilder than a bell curve allows.
Why it mattered
- Computer graphics adopted fractal methods to generate realistic mountains, clouds and plants for film and games.
- Chaos theory gained a visual language, and the Mandelbrot set became a public symbol of mathematical beauty.
- Finance gained a critique of bell-curve models, as Mandelbrot argued that markets show wild, heavy-tailed swings.
- Scientists gained a way to measure roughness in coastlines, tissues and surfaces with a fractal dimension.
Sources
- Benoit Mandelbrot Britannica
- Fractal Britannica
- How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension Science (1967), via Humboldt State University
Community notes
Loading notes…