## The Pattern Book: Fractals, Art, and NatureThis book will allow you to travel through time and space. To facilitate your journey, the editor has scoured the four corners of the earth in a quest for unusual people and their fascinating patterns. From Mozambique, to Asia, to many European countries, the contributors to The Pattern Book include world-famous cancer researchers, little-known artists and eclectirc computer programmers. Some of the patterns are ultramodern, while others are centuries old. Many of the patterns are drawn from the universe of mathematics. Computer recipes are scattered throughout.Although the emphasis is on computer-generated patterns, the book is informal and the intended audience spans several fields. The emphasis is on the fun that the true pattern lover finds in doing, rather than in reading about the doing! The book is organized into three main parts: Representing Nature (for those patterns which describe or show real physical phenomena, e.g., visualizations of protein motion, sea lilies, etc.), Mathematics and Symmetry (for those patterns which describe or show mathematical behavior, e.g. fractals), and Human Art (for those patterns which are artistic works of humans and made without the aid of a computer, e.g. Moslem tiling patterns.) |

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### Contents

Evolution of the Solar and Planetary Vortices | 3 |

Trajectories of a Neural Network Quantizer in Rhythm Space | 18 |

Broccoli Minaret | 28 |

RNA Structure Based on Prime Number Sequence | 42 |

Goldbachs Comet | 55 |

3DCubes | 60 |

The Reversible GreenbergHastings Cellular Automaton | 74 |

Locked Links | 87 |

A Multiple Decomposition Mapping | 228 |

Nevada Sets | 233 |

Julia Iteration z z2 + c | 246 |

Stripes 260 | 256 |

An Octahedral Fractal | 273 |

TriHadamards | 288 |

Fractal Limit A Fractal Pattern Emulating M C Escher | 290 |

Inflation Rules 3 | 304 |

An Iteration Map | 103 |

Voronoi Fractal | 116 |

Modified Logistic Map in the Plane | 120 |

An Asymmetric Sierpinski Carpet | 135 |

Mappings from Recursion of the Function | 151 |

Multiple Decomposition | 155 |

Unrolling the Mandelbrot Set | 169 |

Embellished Lissajous Figures | 183 |

Swirl | 197 |

11 | 199 |

Mappings of the Transcendental Function | 215 |

Bistable Tiling Patterns with ConvergingDiverging Arrows | 317 |

Vivid Depth Percepts from Simple GrayLevel Line Patterns | 319 |

Hyperbolic Tilings | 339 |

Rotation | 353 |

Patterns Composed with Squares | 362 |

An Informal Tesselation of Cats | 375 |

Horoscope | 388 |

Ambiguous Art | 391 |

Art Deco Design 1 | 407 |

425 | |

### Common terms and phrases

A. K. Dewdney algorithm artists attractor axis Beauty behavior biomorphs bounded set C. A. Pickover cells cellular automata Chaos chaotic circle color complex number complex plane Computer Graphics contour coordinates cosh(z created cubes curve Described designs displayed divergent points dots Dover drawing dynamical systems equations escape radius example Figure 1 shows Fractal Geometry fractions function gasket Geometry of Nature grid hexomino I. D. Entwistle imaginary initial integer iteration itermax Julia set L-systems level set Level Set Method M. C. Escher magnification Mandelbrot set mathematical method mosaic ornaments parameter pattern showing Peitgen Penrose tiling pixel plotted polygons polynomial prime produce random recursion References region represents result rotation rule Saupe Science of Fractal screen Sea Horse Valley self-similar sequence shapes shown sinh(z space spiral square structure symmetry triangle Unseen World St variable vertices visual W. H. Freeman