Reading: pg. 525-548

**1.** A magnitude 5.0 earthquake releases roughly 2.05x10^13 ergs of energy; a
magnitude 6.0 earthquake releases roughly 6.4x10^13 ergs. If the power law which states that
P(E) is approximately proportional to E^(-3/2) is a good model, plot the likelihood of
seeing earthquakes of various energies. Repeat for the crater model which states that P(A) is
approximately proportional to 1/A (over some appropriate range of areas).

**2.** Some natural satellites (for example, some Jovian moons) appear to follow a crater power law
such that P(A>a) is proportional to a^-g, where g is slightly greater than 1. Contrast
the case g=1 with the case g>1 for this power law. What would be the difference in
the surfaces?

**3.** Suggest a reasonable implementation of the boid flocking rules; that is,
provide rules for separation, alignment, and cohesion which include specific ranges,
rates at which the adjustments are to be made, and so on. Explain your reasoning.

**4.** What is the perimeter-area relation (P/sqrt(A)) for a square? Is there one value of P/sqrt(A) for all rectangles? Find the value for an equilateral triangle. Does this value
work for all (not necessarily equilateral) triangles?

**5.** What are some strengths and weaknesses of fractal forgeries as a means of generating landscapes?

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