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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a₁ addresses affine transformations Answers to Chapter attractor ball boundary Cantor set Cauchy sequence code space Collage Theorem color compact metric space computed contains continuous function contraction mapping contractivity factor converges coordinates corresponding countable d₁ defined Definition denote distance equation Escape Time Algorithm Euclidean metric Examples & Exercises f₁ filled Julia set finite follows fractal dimension fractal interpolation function fractal system graph Hausdorff Hence homeomorphism hyperbolic illustrated in Figure intersection interval invariant measure invertible iterated function systems just-touching Lemma Let f limit point Mandelbrot set metric equivalence Michael Barnsley Möbius transformation nonempty numits open set orbit parameter space picture pixel Plate polynomial Program radius Random Iteration Algorithm real numbers recurrent shift dynamical system Show Sierpinski triangle similitude sphere subset Suppose symbols totally disconnected w₁ w₁(A w₁(x w₁(z w₂ X₁