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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