Reading: pg. 457-490
1. Use the Collage Theorem to create an IFS for the rectangle with vertices at (0,0), (0,1), (3,1), and (3,0). Then randomize your IFS (see pg.302 of the text), and submit a plot of the results. Repeat with a different collage for the same shape.
2. Use the Collage Theorem to create an IFS for the Koch curve. Then randomize your IFS, and submit a plot of the results.
3. Use the IFS code on pg.258 of the text to generate the fractal twig. (See pg.235-237 for the notation.) Then randomize your IFS, and submit a plot of the results.
4. Use the IFS code on pg.255 of the text to generate the Barnsley fern. (See pg.235-237 for the notation.) Randomize it in several different ways, including according to the ratio of the determinants (as discussed in class); which one looks the best? Submit plots of your results.
5. Run Conway's Game of Life several times. Is there any sense in which the stable structures display self-similarity or represent invariant sets?
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