Mathematical Experiment 13

  1. A harmonic function defined on a graph G is a scaler-valued function f defined on the set of all veritces of G such that f(v) is the average of all f(w) as w ranges over all neighboring vertices of v. We can immitate the boundary-valued problem in analysis by assigning f(x) as x ranges over the endpoints of G and try to solve for f(x) as x ranges over all vertices of G.
    1. Design a graph and assign the boundary values at the endpoints.
    2. Find an approximation method that would give an approximate solution to the boundary-value problem.
  2. Write a program to play the Game of Life.
  3. Write a program to play the Game of Life on some graph.
  4. Draw Mandelbrot's square snowflake.
  5. Display various cross intersection of a torus with a plane.