Fractal geometry and the Mandelbrot set
Geometría fractal y conjunto de Mandelbrot
- Date
- 1975-1980 · confidence high
- Place
- Yorktown Heights, New York (IBM), United States
- Credited to
- Benoît Mandelbrot (Les objets fractals, 1975; the Mandelbrot set, 1980); complex dynamics of Julia and Fatou (1918)
- People
- 👤 Benoît Mandelbrot1924–2010
- Field
- Knowledge & symbols
⚠️ Disputed: the sources disagree.
What was discovered
Concept of objects with non-integer dimension and self-similarity (coastlines, clouds, markets), and the computer visualisation of the Mandelbrot set, of infinite complexity, generated by the iteration z -> z^2 + c.
Julia sets and the study of complex iteration date from 1918; Mandelbrot contributed the unifying concept, the visualisation and the name. Brooks and Matelski drew the set in 1978.
What it led to
- modern complex dynamics (Douady, Hubbard, Yoccoz)
- multifractal analysis
- models of markets and turbulence
- chaos theory
- Computer graphics for landscapes and special effects
- Popular chaos theory and the science of complexity
- Fractal antennas in mobile phones and market analysis
Built on
- Julia set1918
- Koch curve, Cantor set, Sierpiński dust
- Julia and Fatou
- Richardson (coastline length)
- Julia sets
- computer graphics
- chaos theory (Lorenz, 1963)
Made possible
- fractal image compression
- fractal antennas
- computer-generated landscapes
- computer-generated landscapes
- financial market models