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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,
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.
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.