Mathematica Tutorials

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.

Graph Approximations


Magnetic Spectrum

Sierpinski Gasket

Harmonic Sierpinski Gasket

Harmonic Function

Eigenfunction Plots

3D Eigenfunctions