# Barnsley fern

The *Barnsley fern ^{}* $F$ is the only non-empty compact subset of ${\mathbb{R}}^{2}$ satisfying
the relation

$$F=\bigcup _{i=1}^{4}{T}_{i}(F)$$ |

where ${T}_{i}:{\mathbb{R}}^{2}\to {\mathbb{R}}^{2}$ are the following linear mappings:

${T}_{1}(x,y)$ | $=(0.85x+0.04y,-0.04x+0.85y+1.6),$ | ||

${T}_{2}(x,y)$ | $=(0.2x-0.26y,0.23x+0.22y+1.6),$ | ||

${T}_{3}(x,y)$ | $=(-0.15x+0.28y,0.26x+0.24y+0.44),$ | ||

${T}_{4}(x,y)$ | $=(0,0.16y).$ |

Title | Barnsley fern |
---|---|

Canonical name | BarnsleyFern |

Date of creation | 2013-03-22 16:05:33 |

Last modified on | 2013-03-22 16:05:33 |

Owner | paolini (1187) |

Last modified by | paolini (1187) |

Numerical id | 7 |

Author | paolini (1187) |

Entry type | Example |

Classification | msc 28A80 |