These classic fractals were generated as applications of L-systems, starting with the axiom, using the string replacement rules listed under each corresponding figure, and making turns according to the angle specified. All symbols are replaced simultaneously; those without replacement rules are retained unaltered. The symbols are interpreted as in "Turtle Graphics":

Symbol | Interpretation |
---|---|

F G L R S X Y Z | move and draw line |

@ | move but don't draw |

+ | turn to the left |

- | turn to the right |

[ | begin side branch |

] | end side branch |

Radial snowflake | Sierpinski arrowhead | Sierpinski gasket | Sierpinski curve |

Koch snowflake | Koch island | Koch mosaic | Koch curve |

Hilbert curve | Peano S curve | Dragon curve | Gosper curve |