1 Horror Vacui 2 A Very Patient Turtle Who Draws Lines 3 A Taxonomy of Fractology 4 Gallery of Specimens |

Root 2 Family | Root 3 Family | Root 4 Square Grid Family | Root 4 Triangle Grid Family |

Root 5 Family | No Root 6! | Root 7 Family | Root 8 Family |

Root 9 Square Grid Family | Root 9 Triangle Grid Family | Root 10 Family | Root 12 Family |

Root 13 Square Grid Family | Root 13 Triangle Grid Family | Root 16 Square Grid Family | Root 16 Triangle Grid Family |

Root 17 and Beyond... | 5 My Brain Fillith Over | 6 References | 7 Acknowledgements |

It is time to officially introduce the first family of fractal curves: the root2 family. The first specimen I will show you is perhaps the most famous one of all: the classic dragon curve. Mandelbrot called it the "Harter-Heighway Dragon", after two mathematicians who explored it. It is sometimes referred to as the "Jurassic Park Dragon". For convenience, I will just call it the "HH Dragon". The other plane-filling curve of the root2 family is the Polya Sweep. Such a very different fractal! In fact, if we continue to fractalize these two curves to high-level teragons, the HH Dragon becomes increasingly craggy along its boundary, while the Polya Sweep becomes increasingly straight along its three sides. What's up with that? |

End of chapter. |

1 Horror Vacui 2 A Very Patient Turtle Who Draws Lines 3 A Taxonomy of Fractology 4 Gallery of Specimens |

Root 2 Family | Root 3 Family | Root 4 Square Grid Family | Root 4 Triangle Grid Family |

Root 5 Family | No Root 6! | Root 7 Family | Root 8 Family |

Root 9 Square Grid Family | Root 9 Triangle Grid Family | Root 10 Family | Root 12 Family |

Root 13 Square Grid Family | Root 13 Triangle Grid Family | Root 16 Square Grid Family | Root 16 Triangle Grid Family |

Root 17 and Beyond... | 5 My Brain Fillith Over | 6 References | 7 Acknowledgements |

Brain-filling Curves - A Fractal Bestiary
by Jeffrey Ventrella Distributed by Lulu.com Cover Design by Jeffrey Ventrella |
Book web site:
BrainFillingCurves.com
ISBN 978-0-9830546-2-7 Copyright © 2012 by Jeffrey Ventrella |
eyebrainbooks.com |
FractalCurves.com |