5. Self-Similarity and Fractal Geometry

Read the opening pages · printed page 61

Diffusion-Limited Aggregation (diffuse.c)

Particles wander at random until they touch the growing cluster, then freeze. Because a wandering particle is far more likely to bump into a tip than to find its way into a crevice, the cluster grows branches, and the branches grow branches. The result has a fractional dimension of about 1.7, the same as coral, frost, and electrical discharge. Runs alternate between one seed, several seeds, and a line seed along the bottom that grows a forest. Full screen →

Sections

1. The Cantor Set
2. The Koch Curve
3. The Peano Curve
4. Fractional Dimensions
5. Random Fractals in Nature and Brownian Motion
6. Further Exploration
7. Further Reading

Figures

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