- 548 pages
- English
- PDF
- Only available on web
Fractals Everywhere
About This Book
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.
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Table of contents
- Front Cover
- Fractals Everywhere
- Copyright Page
- Table of Contents
- Dedication
- Foreword to the Second Edition
- Acknowledgments
- Chapter I. Introduction
- Chapter II. Metric Spaces; Equivalent Spaces; Classification of Subsets; and the Space of Fractals
- Chapter III. Transformations on Metric Spaces; Contraction Mappings; and the Construction of Fractals
- Chapter IV. Chaotic Dynamicson Fractals
- Chapter V. Fractal Dimension
- Chapter VI. Fractal Interpolation
- Chapter VII. Julia Sets
- Chapter VIII. Parameter Spaces and Mandelbrot Sets
- Chapter IX. Measures on Fractals
- Chapter X. Recurrent Iterated Function Systems
- References
- Selected Answers
- Index
- Credits for Figures and Color Plates