# Difference between revisions of "Field:Fractals"

Line 12: | Line 12: | ||

:* Iterated function systems — These have a fixed geometric replacement rule. Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Heighway dragon curve, T-Square, Menger sponge, are some examples of such fractals. | :* Iterated function systems — These have a fixed geometric replacement rule. Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Heighway dragon curve, T-Square, Menger sponge, are some examples of such fractals. | ||

:* Random fractals — Generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian motion, Lévy flight, fractal landscapes and the Brownian tree. The latter yields so-called mass- or dendritic fractals, for example, diffusion-limited aggregation or reaction-limited aggregation clusters. --[www.wikipedia.org| Wikipedia] | :* Random fractals — Generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian motion, Lévy flight, fractal landscapes and the Brownian tree. The latter yields so-called mass- or dendritic fractals, for example, diffusion-limited aggregation or reaction-limited aggregation clusters. --[www.wikipedia.org| Wikipedia] | ||

− | |||

− | |||

− | + | History, Mandelbrot 1975 | |

+ | Self-similarity | ||

+ | Iterating | ||

+ | complex, <math>z = z^2 + c\,</math> | ||

+ | -to zero = black | ||

+ | -infinity - color, how fast is what color | ||

− | + | Fractal dimension | |

− | |||

− | |||

− | |||

− | + | Examples: Cantor sets, Sierpinski triangle and carpet, Menger sponge, dragon curve, space-filling curve, Koch curve, Lyapunov fractal, and Kleinian groups. | |

− | + | Nature | |

− | |||

− | |||

− | |||

LINKS | LINKS |

## Revision as of 09:13, 1 June 2009

# Fractals

A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."

- General description
- history, self-similarity, iterating

## Contents |
[[Image:|300px|thumb|right|]] |

## Links to Other Information

http://en.wikipedia.org/wiki/Fractals