## Fractal Geometry: Mathematical Foundations and ApplicationsSince its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has been extensively revised and updated. It features much new material, many additional exercises, notes and references, and an extended bibliography that reflects the development of the subject since the first edition. * Provides a comprehensive and accessible introduction to the mathematical theory and applications of fractals. * Each topic is carefully explained and illustrated by examples and figures. * Includes all necessary mathematical background material. * Includes notes and references to enable the reader to pursue individual topics. * Features a wide selection of exercises, enabling the reader to develop their understanding of the theory. * Supported by a Web site featuring solutions to exercises, and additional material for students and lecturers. Fractal Geometry: Mathematical Foundations and Applications is aimed at undergraduate and graduate students studying courses in fractal geometry. The book also provides an excellent source of reference for researchers who encounter fractals in mathematics, physics, engineering, and the applied sciences. Also by Kenneth Falconer and available from Wiley: Techniques in Fractal Geometry ISBN 0-471-95724-0 Please click here to download solutions to exercises found within this title: http://www.wileyeurope.com/fractal |

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afﬁne approximation attractor F Borel set bounded box dimension box-counting dimension Brownian motion Cantor dust closed compact construction contains converges Corollary countable deﬁne deﬁnition denote difﬁculties dimB dimBF dimH dimHF disjoint dynamical systems equations estimate example ﬁgure ﬁnd ﬁne ﬁnite ﬁrst ﬁxed point fk(z ﬂuid follows Fractal Geometry given graph Hausdorff and box Hausdorff dimension Hausdorff measures Hs(F inﬁnitely integer intersection invariant irregular 1-set iterated function system J(fc Julia set Koch curve kth level intervals Lebesgue measure Legendre transform Lemma Let F line segment Mandelbrot mapping mass distribution mathematics middle third Cantor multifractal non-empty open set orbit plane point of f polynomial positive probability Proof properties Proposition random variable real numbers s-set satisﬁes self-afﬁne self-similar self-similar measure sequence set F Show similar square subset Theorem theory third Cantor set transformation upper box dimension zero