A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline measured with different length rulers. The shorter the ruler, the longer the length measured, a paradox known as the coastline paradox.

Illustrated above are the fractals known as the Gosper island, Koch snowflake, box fractal, Sierpiński sieve, Barnsley's fern, and Mandelbrot set.

See also

Attractor, Backtracking, Barnsley's Fern, Box Fractal, Cactus Fractal, Cantor Dust, Cantor Set, Cantor Square Fractal, Carotid-Kundalini Fractal, Cesàro Fractal, Chaos Game, Circles-and-Squares Fractal, Coastline Paradox, Dendrite Fractal, Dragon Curve, Fat Fractal, Fatou Set, Fractal Dimension, Gosper Island, H-Fractal, Hénon Map, Iterated Function System, Julia Set, Kaplan-Yorke Map, Koch Antisnowflake, Koch Snowflake, Lévy Fractal, Lévy Tapestry, Lindenmayer System, Lorenz Attractor, Mandelbrot Set, Mandelbrot Tree, Menger Sponge, Minkowski Sausage, Mira Fractal, Newton's Method, Pentaflake, Peano Curve, Peano-Gosper Curve, Pythagoras Tree, Rabinovich-Fabrikant Equation, Rep-Tile, San Marco Fractal, Self-Similarity, Siegel Disk Fractal, Sierpiński Carpet, Sierpiński Curve, Sierpiński Sieve, Star Fractal, Strange Attractor, Zaslavskii Map Explore this topic in the MathWorld classroom

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Weisstein, Eric W. "Fractal." From MathWorld--A Wolfram Web Resource.

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