## Fractals EverywhereThis volume is the revised second edition of the original book, published in 1988. It includes additional problems and tools emphasizing fractal applications, as well as an all-new answer key to the text exercises. The revision incorporates new chapters on vector recurrent iterated function systems and application of fractals. It also contains an extended chapter on dynamical systems. Input from advisors and potential adopters should make it more suitable for use as a textbook. |

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### Contents

Chapter Introduction | 5 |

Cauchy Sequences Limit Points Closed Sets | 15 |

Connected Sets Disconnected Sets and Pathwise | 24 |

Copyright | |

12 other sections not shown

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addresses affine transformations Algorithm applied approximately associated attractor ball Barnsley Borel boundary bounded called Chapter choose closed code space color compact metric space complete computed condition connected Consequently Consider construct contains continuous converges coordinates corresponding defined Definition denote described distance dynamical system equal equation equivalent Escape Euclidean example Examples & Exercises exists factor field Figure finite fixed point follows fractal dimension function geometrical given gives graph Hence hyperbolic illustrated implies integer interval invariant invertible Iteration Julia set limit look means measure metric space obtain operator orbit origin parameter period picture plane positive probabilities Program proof prove provides Random region represented result scaling sequence shift dynamical system Show sphere subset Suppose symbols Table Theorem totally disconnected