## Indra's Pearls: The Vision of Felix KleinFelix Klein, one of the great nineteenth-century geometers, rediscovered in mathematics an idea from Eastern philosophy: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple co-existing symmetries. For a century these ideas barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research. |

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#### LibraryThing Review

User Review - fpagan - LibraryThingMathematical and algorithmic details of a lesser-known class of fractals. Quite lavishly produced. Read full review

### Contents

The language of symmetry | 1 |

A delightful fiction | 36 |

Double spirals and Möbius maps | 62 |

The Schottky dance | 96 |

Fractal dust and infinite words | 121 |

Indras necklace | 157 |

The glowing gasket 196 | 196 |

### Other editions - View all

Indra's Pearls: The Vision of Felix Klein David Mumford,Caroline Series,David Wright Limited preview - 2002 |

Indra's Pearls: The Vision of Felix Klein David Mumford,Caroline Series,David Wright No preview available - 2015 |

Indra's Pearls: The Vision of Felix Klein David Mumford,Caroline Series,David Wright No preview available - 2002 |

### Common terms and phrases

abab algebra algorithm angle Apollonian gasket blue boundary calculate called centre chain Chapter coloured complex numbers conjugate corresponding curve cusp groups cyclic permutations depth-first search double cusp equation exactly example Farey Farey sequence fixed point formula fractal fractions frame of Figure Fuchsian geometry half plane Hausdorff dimension hyperbolic ideal triangle infinite words inside integer inverse Klein Kleinian groups labelled limit points limit set look loop loxodromic Maskit mathematical mathematician matrix Möbius maps Möbius transformations modular group move multiply nesting non-Euclidean º º º ordinary set pair parabolic parameters pattern picture plot pſa quasicircle radius real numbers region repetends Riemann sphere rotation Schottky circles Schottky disks Schottky group segment sequence shows slice spiral stereographic projection Stickler symmetry tangency points tangent tangent circles tile torus trace translation unit circle vertical word tree