7. Affine Transformation Fractals

Read the opening pages · printed page 95

Iterated Function Systems (ifs.c (and mrcm.c))

A handful of affine maps, each one a shrink, rotate, and shift, played as a chaos game: pick a map at random, apply it to the current point, plot, repeat. The cloud of points converges onto the one shape that all the maps together leave unchanged. The fern, the tree, the snowflake, and the dragon here are each just three to six lines of numbers from the book's data file. Between shapes the numbers are interpolated, so the attractor itself morphs, passing through strange intermediate forms that no one designed. Full screen →

Sections

1. A Review of Linear Algebra
2. Composing Affine Linear Operations
3. The Multiple Reduction Copy Machine Algorithm
4. Iterated Functional Systems
5. Further Exploration
6. Further Reading

Figures

Figure 7.1Figure 7.2Figure 7.3Figure 7.4Figure 7.5Figure 7.6Figure 7.7Figure 7.8Figure 7.9Figure 7.10Figure 7.11Figure 7.12Figure 7.13Figure 7.14Figure 7.15Figure 7.16Figure 7.17