Fractal Geometry
Mandelbrot (1975-82) shows that coastlines, clouds and the Mandelbrot set share self-similar shapes of fractional dimension, and that computers can draw them.
Open in the interactive tree →Mathematicians had met such shapes since Weierstrass (1872), Cantor (1883), Koch (1904) and Sierpinski (1915), and Fatou and Julia studied iterated complex maps in 1918. Benoit Mandelbrot asked in 1967 how long the coast of Britain is (the answer depends on the ruler), coined 'fractal' in 1975, published the Mandelbrot set in 1980 using IBM computers and brought the field to a wide public with The Fractal Geometry of Nature (1982). Loren Carpenter showed fractally generated landscapes at SIGGRAPH in 1980; fractals now appear in computer graphics, antenna design, image compression and medical imaging.
Prerequisites
- Complex Numbers1545The Mandelbrot set comes from iterating a formula on complex numbers.
- Programmable Computer (Zuse Z3)1941Mandelbrot's pictures needed IBM computers to draw.
- Chaos Theory1963Fractal dimension describes the shapes that chaotic systems trace out.