Author | Peitgen, Heinz-Otto. author |
---|---|
Title | Fractals for the Classroom: Strategic Activities Volume One [electronic resource] / by Heinz-Otto Peitgen, Hartmut Jรผrgens, Dietmar Saupe, Evan Maletsky, Terry Perciante, Lee Yunker |
Imprint | New York, NY : Springer New York, 1991 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9047-3 |
Descript | XII, 129 p. 37 illus. online resource |
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 Pascalโs 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