• harmonicextender.m prompts the user to input the level SC, and four functions to be defined on each of the edges.  MATLAB then computes the harmonic extension on SC.
• SCenergy.m  takes any function defined on any m'th level SC and calculates the graph energy of that function.

6 examples of harmonic extension with 0 defined on 3 edges and sin(π kx) on the fourth

download the .mat file here

Restrictions of the harmonic functions alongthe line one-third of the way from the nonzero boundary edge.

Poisson Kernel

click here to download MATLAB .mat data used in paper.

click here for MATLAB scripts used to generate Figure 3.6 in paper

click here for the MATLAB script that generates effective resistances with a fixed stimulus point.

click here to download some of the MATLAB .mat data used in paper