Fractal Worlds, a text by
Michael Frame and Amelia Urry 
Mandelbrot's 2010 TED talk 
Frame's 2013 TEDxYale talk 
Fractal geometry coursepage 
Java Software 
Panorama of Uses 

1. Introduction to Fractals 
1A. SelfSimilarity 
1B. More Examples of SelfSimilarity 
1C. Initiators and Generators 
1D. Geometry of Plane Transformations 
1E. Iterated Function Systems 
1F. Inverse Problems 
1G. Random IFS 
1H. Driven IFS 
1I. Architecture 
2. Natural Fractals and Dimensions 
2A. Ineffective Ways to Measure 
2B. BoxCounting Dimension 
2C. Similarity Dimension 
2D. The Moran Formula 
2E. Other Dimensions 
2F. AreaPerim 
2G. Dim Algebra 
2H. Natural Fractals 
2I. Manufactured Fractals 
3. The Mandelbrot Set and Julia Sets 
3A. Complex Iteration 
3B. Julia Sets 
3C. The Mandelbrot Set 
3D. Combinatorics of the Mandelbrot Set 
3E. The Boundary of the Mandelbrot Set 
3F. Scalings in the Mandelbrot Set 
3G. Complex Newton's Method 
3H. Universality of the Mandelbrot Set 
3I. Mandelbrot Monk 
3J. Fractals in Literature 
3K. Fractals in Art 
4. Cellular Automata and Fractal Evolution 
4A. SelfReplicating Machines 
4B.Cellular Automata Basics 
4C. Cellular Automata Patterns 
4D. Genetic Algorithms 
4E. Fractal Fitness Landscapes 
4F. 1/f Noise 
4G. Music, including 1/f 
4H. Fractal History

4I. Video Feedback 
4J. Leopard Spots 
4K. Neural Nets 
4L. Artificial Life 
5. Random Fractals and the Stock Market 
5A. SelfSimilar Distributions 
5B. Brownian Motion 
5C. Fractional Brownian Motion 
5D. Levy Flights 
5E. DiffusionLimited Aggregation 
5F. Percolation 
5G. Bacterial Growth 
5H. Galaxy Distributions 
5I. Internet Traffic 
5J. Random Fractal Cartoons 
5K. Stock Market Surrogates 
6. Chaos 
6A. Doubling 
6B. Introduction to Chaos 
6C. Test Functions 
6D1. Graphical Iteration 
6D2. Time Series 
6D3. Histograms 
6D4. Bifurcation Diagrams 
6D5. Return Map 
6D6. Driven IFS 
6D7. Kelly Plot 
6E. Fixed Points 
6F. Cycles 
6G. Perioddoubling Bifurcation 
6H. Chaos Definition 
6I. Dust in the Tent Map 
6J. Tent and Logistic Bifurcation Diagrams 
6K. Tangent Bifurcation 
6L. Intermittency 
6M. Discontinuous Bifurcations 
6N. Scaling 
6O. Universality 
6P. Renormalization 
6Q. Driven IFS 
6R. Kelly Plot 
6S. Control of Chaos 
6T. Synchronization of Chaotic Processes 
7. Multifractals 
7A. Unequal Probabilities 
7B. Histograms 
7C. Another Example 
7D. Local Dimensions 
7E. Multifractals from IFS 
7F. f(a) curves 
7G. f(a) from financial data 
8. Fractal Trees 
8A. Definitions 
8B. SelfContact 
8C. Dimension 
8D. Animationss 
9. Circle Inversions 
9A. Inversion properties 
9B. Limit Sets 
9C. Overlapping circles 
9D. Animations 
9E. Mandelbrot's Algorithm 
9F. Dimensions 
9G. Restricted Limit Sets 
9H. Driven IFS 
Labs 
Lesson Plans 
Mathematica Notebooks 
School Work 
References 