## Discrete iterated function systemsWritten for researchers and developers applying Integrated Function Systems in the creation of fractal images, this book presents a modification of a widely used probabilistic algorithm for generating IFS-encoded images. The book also includes a discussion of how IFS techniques can be applied to produce animated motion pictures. |

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### Contents

Deterministic Theory of Iterated Function Systems | 9 |

List of Figures | 18 |

Probabilistic Theory of Iterated Function Systems | 39 |

Copyright | |

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### Common terms and phrases

accuracy 1/M affine transformations animation segment applying arccos associated probabilities assumptions attractor Barnsley Cantor set cardinality centered chapter coincides compact subsets complete metric space condensation set consider contraction mapping theorem contractive homothety contractive transformations contractivity factor converge weakly coordinate corresponding data compression defined Definition denotes domains of attraction dragon encoding Equation Euclidean plane example fern Figure finite number formula 4.2 Hausdorff distance Hausdorff metric homothety inequality integer invariance condition invariant distribution irreducible closed set Iterated Function Systems level of accuracy maple leaf Markov chain Markov chain associated minimal absorbing component minimal absorbing set nonempty nonnegative integer obtained orbit origin pixel belonging pixel P(i,j probabilistic process Xn}%L0 proof provides random iteration algorithm round-off process round-off version rounding errors satisfied Section self-covering property sequence shades of grey Sierpinski triangle strict contraction subdomains of attraction subsets of IR2 theory tion unique invariant unique stationary distribution won(x xn+i