Homework #11

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?