Table of Contents

Unit 1 Self-Similarity.- Key Objectives, Notions, and Connections.- Mathematical Background.- Using the Activities Sheets.- 1.1 Sierpinski Triangle and Variations.- 1.2 Number Patterns and Variations.- 1.3 Square Gasket.- 1.4 Sierpinski Tetrahedron.- 1.5 Trees.- 1.6 Self-Similarity: Basic Properties.- 1.7 Self-Similarity: Specifics.- 1.8 Box Self-Similarity: Grasping the Limit.- 1.9 Pascal’s Triangle.- 1.10 Sierpinski Triangle Revisited.- 1.11 New Coloring Rules and Patterns.- 1.12 Cellular Automata.- Unit 2 The Chaos Game.- Key Objectives, Notions, and Connections.- Mathematical Background.- Using the Activities Sheets.- 2.1 The Chaos Game.- 2.2 Simulating the Chaos Game.- 2.3 Addresses in Triangles and Trees.- 2.4 Chaos Game and Sierpinski Triangle.- 2.5 Chaos Game Analysis.- 2.6 Sampling and the Chaos Game.- 2.7 Probability and the Chaos Game.- 2.8 Trees and the Cantor Set.- 2.9 Trees and the Sierpinski Triangle.- Unit 3 Complexity.- Key Objectives, Notions, and Connections.- Mathematical Background.- Using the Activities Sheets.- 3.1 Construction and Complexity.- 3.2 Fractal Curves.- 3.3 Curve Fitting.- 3.4 Curve Fitting Using Logs.- 3.5 Curve Fitting Using Technology.- 3.6 Box Dimension.- 3.7 Box Dimension and Coastlines.- 3.8 Box Dimension for Self-Similar Objects.- 3.9 Similarity Dimension.- Answers.

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