Fractals Everywhere: New Edition

Front Cover
Courier Corporation, Oct 3, 2013 - Mathematics - 560 pages
"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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Contents

Chapter IV
The Addresses of Points on Fractals
Continuous Transformations from Code Space to Fractals
Introduction to Dynamical Systems
Or How to Compute Orbits
Fractal Dimension
Fractal Interpolation
Julia Sets

Möbius Transformations on the Riemann Sphere
Analytic Transformations
How to Change Coordinates
The Contraction Mapping Theorem
Contraction Mappings on the Space of Fractals
Two Algorithms for Computing Fractals from Iterated Function Systems
Condensation Sets
How to Make Fractal Models with the Help of the Collage Theorem
The Continous Dependence of Fractals on Parameters
Parameter Spaces and Mandelbrot Sets
Measures on Fractals
Recurrent Iterated Function Systems
References
Selected Answers
Index
Credits for Figures and Color Plates
Copyright

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About the author (2013)

Michael F. Barnsley is a British mathematician, researcher, and author who holds several patents on fractal compression. He is a faculty member of the Mathematical Sciences Institute at Australian National University, and he previously taught in the United States at Georgia Tech.

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