Exploring fractals on the Macintosh Book

	Preface
Ch. 1	Fractals in Our World	1
	Fractals in Nature	2
	Fractals in Science	6
	Fractals in the Arts	10
	Fractals and Computers	16
Ch. 2	Basics of Fractals	19
	What Is Fractal Geometry?	19
	What Is a Linear Fractal?	21
	What Is a Nonlinear Fractal?	22
	What Is Fractal Dimension?	23
	Where Are Fractals Being Used Today?	24
	What Is Chaos Mathematics?	25
Ch. 3	Creating Classical Fractals on the Macintosh	27
	FractaSketch: A Tool for Exploring Fractal Geometry	28
	The Cantor Set: Mathematical Dust	30
	The Peano Curve	35
	The Hilbert Curve	42
	The Koch Curve	45
	The Pascal Triangle Passed to Sierpinski	51
	The Dragon Curve	57
	Finite Segments and Proportional Widths	63
Ch. 4	Calculating Fractal Dimensions	75
	Mathematical Tools	76
	The Hausdorff-Besicovitch Dimension	78
	Calculating Traditional Dimensions	78
	Calculating Dimensions of Self-Similar Fractals	80
	The Richardson Method of Varied Measured Lengths	92
	The Box-Counting Method	99
Ch. 5	Exploring Nonlinear Fractals with MandelMovie	109
	The Mandelbrot Set	110
	Using MandelMovie to Explore the Mandelbrot Set	119
	Julia Sets	121
	Exploring Julia Sets with MandelMovie	127
Ch. 6	Fractals That Fell through the Cracks	131
	The Infinite Staircase	131
	Newton's Method	134
	Randomness and Its Staggering Results	139
	Fractal Mountains and Fractal Clouds	145
	Multifractals	149
	Fractal Image Compression	149
	Aggregate Growth: The Fractal of Crystals	151
	Iterated Function Systems	155
Ch. 7	Recipes from the Fractal Cookbook	187
	The Basic Algorithm	187
	The Relationships with Lindenmayer Systems	190
	Techniques to Increase Speed and Accuracy	192
	The Technique of Faking It	198
	Calculating the Fractal Dimension	200
	Low-Level Information about FractaSketch	203
Ch. 8	Creating Programs to Explore Fractals and Chaos	207
	PostScript Code for Generating High-Resolution Linear Fractals	207
	Algorithms for Mandelbrot and Julia Sets	215
	C Code for Plotting Newton's Method	225
	C Code for IFS Transformations	238
	Basic Programs for Drawing Fractals and Creating Chaos Models	241
	Creating Fractal Models with Mathematica	278
Ch. 9	FractaSketch User Manual	283
	Basic Features	283
	Overview of the Menu Commands	287
	Added Features Found in Extended Versions of FractaSketch	292
	Tips and Techniques	292
Ch. 10	MandelMovie User Manual	297
	Basic Features	297
	Overview of the Menu Commands	302
	Added Features Found in Extended Versions of MandelMovie	317
	Appendix A The Fractal Gallery	323
	Benoit Mandelbrot's World	323
	Inkblots of Nature	325
	Fractal Potpourri	328
	Appendix B Graph Paper with Different Grid Sizes	331
	Appendix C Video Feedback	333
	Works Cited	335
	List of Contributors	341
	Index	345