Mathematica Tutorials

• Intro to Mathematica
  • Courtesy of Alex Baldenko
  • This file is an introduction to mathematica.

N-Gasket Approximations

• Graph Approximations , Computable Document Format
  • Courtesy of Jason Marsh
  • This notebook creates graph approximations to N-gaskets as in the paper by B. Boyle, K. Cekala, D. Ferrone, N. Rifkin and A. Teplyaev, here.
• Eigenfunctions
  • This notebook plots the values of the eigenfunctions of an N-gasket fractal.
• Eigenplots, CDF Version
  • These notebooks construct eigenvector coordinate plots for the N-gaskets above.
• Harmonic Coordinates
  • This notebook plots harmonic coordinates for the N-gasket of your choice. Note that the harmonic coordinates are only injective for the Sierpinski gasket -(1,1,1).

Magnetic Transformation of the Laplacian

• Sierpinski Gasket, Hexagasket, Nonagasket
  • These notebooks plot the spectra of magnetic perturbations of the standard Laplacian on the Sierpinski (resp hexa-, nona-) gasket as the phase of the field changes. This is along the lines of the 3rd section of the paper "Renormalization group analysis and quasicrystals" by Jean Bellissard.