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In mathematics, a chaotic map is a map that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.

Chaotic maps often generate fractals. Although a fractal may be constructed by an iterative procedure, some fractals are studied in and of themselves, as sets rather than in terms of the map that generates them. This is often because there are several different iterative procedures to generate the same fractal.

List of chaotic maps

List of fractals

• Cantor set
• Gravity set, or Mitchell-Green gravity set
• Julia set - derived from complex quadratic map
• Koch snowflake
• Lyapunov fractal
• Mandelbrot set - derived from complex quadratic map
• Menger sponge
• Sierpinski carpet
• Sierpinski triangle

• Mathematics
• Chaos
• Chaotic maps
• Mathematics-related lists