Fractals EverywhereAcademic Press, 2014 M05 10 - 548 pages Fractals Everywhere, Second Edition covers the fundamental approach to fractal geometry through iterated function systems. This 10-chapter text is based on a course called "Fractal Geometry", which has been taught in the School of Mathematics at the Georgia Institute of Technology. After a brief introduction to the subject, this book goes on dealing with the concepts and principles of spaces, contraction mappings, fractal construction, and the chaotic dynamics on fractals. Other chapters discuss fractal dimension and interpolation, the Julia sets, parameter spaces, and the Mandelbrot sets. The remaining chapters examine the measures on fractals and the practical application of recurrent iterated function systems. This book will prove useful to both undergraduate and graduate students from many disciplines, including mathematics, biology, chemistry, physics, psychology, mechanical, electrical, and aerospace engineering, computer science, and geophysical science. |
Contents
| 1 | |
| 5 | |
| 42 | |
Chapter IV Chaotic Dynamicson Fractals | 115 |
Chapter V Fractal Dimension | 171 |
Chapter VI Fractal Interpolation | 205 |
Chapter VII Julia Sets | 246 |
Chapter VIII Parameter Spaces and Mandelbrot Sets | 294 |
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Common terms and phrases
addresses affine transformations Answers to Chapter attractor ball boundary Cantor set Cauchy sequence choose closed code space Collage Theorem compact metric space computed connected contains continuous function contraction mapping contractivity factor converges coordinates corresponding countable defined Definition distance dynamical system associated equation Escape Time Algorithm Euclidean metric Examples & Exercises filled Julia set finite follows fractal dimension fractal interpolation function fractal system function f geometrical given graph Hence homeomorphism hyperbolic illustrated in Figure intersection interval invariant measure invertible Iterated Function Systems just-touching Let f limit point Mandelbrot set Markov operator metric equivalence Michael Barnsley Möbius transformation nonempty numits open set parameter space pixel plane point x e polynomial Program radius Random Iteration Algorithm real numbers recurrent set of points shift dynamical system Show Sierpinski triangle similitude sphere Suppose symbols totally disconnected transformation f