On-line Books
Exploring Fractals on the Macintosh
By Bernt Wahl, Peter Van Roy, Michael Larsen and Eric Kampman.
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Dedication
Preface
Chapter 1: Fractals In Our World
Fractals in Nature
Fractals in Science
Fractals in the Arts
Fractals and Computers
Chapter 2: Fractals Basics
What Is Fractal Geometry?
What Is a Linear Fractal?
What Is a Non-Linear Fractal?
What Is Fractal Dimension?
Where are Fractals Being Used Today?
What Is Chaos Mathematics?
Chapter 3: Creating Classical Fractals on the Macintosh
FractaSketch: A Tool for Exploring Fractal Geometry
The Cantor Set: Mathematical Dust
The Peano Curve
The Hilbert Curve
The Koch Curve
The Pascal Triangle Passed to Sierpinski
The Dragon Curve
Finite Segments and Proportional Widths
Chapter 4: Calculating Fractal Dimensions
Mathematical Tools
The Hausdorff-Besicovitch Dimension
Calculating Traditional Dimensions
Calculating Dimensions of Self-Similar Fractals
The Richardson Method of Varied
Measured Lengths
The Box Counting Method
Chapter 5: Exploring Non-Linear Fractals with MandelMovie
The Mandelbrot Set
Using MandelMovie to Explore the Mandelbrot Set
Julia Sets
Exploring Julia Sets with MandelMovie(TM)
Chapter 6: Fractals That Fell through the Cracks
The Infinite Staircase
Newton's Method
Randomness and Its Staggering Results
Fractal Mountains and Fractal Clouds
Multi-fractals
Fractal Image Compression
Aggregate Growth: the Fractal of Crystals
Iterated Function Systems
Chapter 7: Recipes from the Fractal Cookbook
The Basic Algorithm
The Relationship with Linenmayer Systems
Techniques to Increase Speed and Accuracy
The Technique of Facking It
Calculating The Fractal Dimension
Low-Level Information about FractaSketch
Chapter 8: Creating Programs to Explore Fractals and Chaos
PostScript Code for Generating High-Resolution Linear Fractals
Algorithms for Calculating
Mandelbrot and Julia Sets
C Code for Plotting Newton's Method
C Code for IFS Transformations
Basic Programs for Drawing Fractals and Creating Chaos Models
Creating Fractal Models with Mathematics
Chapter 9: FractaSketch User Manual
Basic Features
Overview of the Menu Commands
Added Features Found in Extended Versions of FractaSketch
Tips and Techniques
Chapter 10: MandelMovie User Manual
Basic Features
Overview of the Menu Commands
Added Features Found in Extended Versions of MandelMovie
Appendix A
The Fractal Gallery
Benoit Mandelbrot's World
Inkblots of Nature
Fractal Potpourri
Appendix B
Graph Paper with Different Grid Sizes
Appendix C
Video Feed Back
Works Cited
List of Contributors
Index
Bibliography
Acknowledgments
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