Fractals Everywhere"Difficult concepts are introduced in a clear fashion with excellent diagrams and graphs." — Alan E. Wessel, Santa Clara University "The style of writing is technically excellent, informative, and entertaining." — Robert McCarty This new edition of a highly successful text constitutes one of the most influential books on fractal geometry. An exploration of the tools, methods, and theory of deterministic geometry, the treatment focuses on how fractal geometry can be used to model real objects in the physical world. Two sixteen-page full-color inserts contain fractal images, and a bonus CD of an IFS Generator provides an excellent software tool for designing iterated function systems codes and fractal images. Suitable for undergraduates and graduate students of many backgrounds, the treatment starts with an introduction to basic topological ideas. Subsequent chapters examine transformations on metric spaces, dynamics on fractals, fractal dimension and interpolation, Julia sets, and parameter spaces. A final chapter introduces measures on fractals and measures in general. Problems and tools emphasize fractal applications, and an answers section contains solutions and hints. |
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addresses affine transformations Answers to Chapter attractor ball Barnsley Borel measure boundary Cantor set Cauchy sequence code space Collage Theorem compact metric space computed connected contains continuous function contraction mapping contractivity factor converges coordinates corresponding countable defined definition distance equation Escape Time Algorithm Euclidean metric Examples & Exercises field figure filled Julia set find finite first follows fractal dimension fractal interpolation function fractal system function f given graph Hausdorff Hence homeomorphism hyperbolic illustrated in Figure infinite intersection interval invariant measure invertible Iterated Function Systems Julia set just-touching Lemma Let f limit point Mandelbrot set Manhattan metric Markov operator metric equivalence Michael Bamsley Michael Barnsley numits open set parameter space picture pixel polynomial Program radius Random Iteration Algorithm real numbers recurrent shift dynamical system Show Sierpinski triangle similitude sphere subset Suppose symbols totally disconnected transformation f