Mathematical Experiment 13

A harmonic function defined on a graph G is a scalervalued 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 boundaryvalued 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.

Design a graph and assign the boundary values at the endpoints.

Find an approximation method that would give an approximate solution to
the boundaryvalue problem.

Write a program to play the Game of Life.

Write a program to play the Game of Life on some graph.

Draw Mandelbrot's square snowflake.

Display various cross intersection of a torus with a plane.