Homework 4


Homework 4: Due Tuesday October 26

  1. Understanding Nonlinear Dynamics, problem 2.5. If you wish, you may use one of the CA programs on the web to help you with this. (15 points)
  2. Understanding Nonlinear Dynamics, problem 2.6. (15 points)
  3. Convert 311 to binary. (5 points)
  4. How many possible 1d two-state CAs are there with radius 3? (5 points)
  5. Find a big map of the coast of Maine. (There's a nice map outside Craig Greene's office.) Measure the length of the coast using successively smaller "sticks" of length epsilon. Use the relation between total length and epsilon to estimate the box-counting dimension. Your estimate should also include an estimate of your error. This web site might be helpful.(20 points)
  6. Calculate the fractal dimension of the following objects.
    1. The Sierpinski Sponge.
    2. A Fractal Tree.
  7. Find a fractal on the web, in a book, or in "real life". Write a short paragraph about it. Your write up should include some statement about the dimension of the object. Cite any sources.


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