# Difference between revisions of "Field:Fractals"

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:* 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 | + | *History, Mandelbrot 1975 |

− | Self-similarity | + | *Self-similarity |

− | Iterating | + | **Iterating |

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

− | + | ***to zero = black | |

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

− | Fractal dimension | + | *Fractal dimension |

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

Nature | Nature |

## Revision as of 09:14, 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