The following images are contour plots of the first 24 eigenfunctions (ordered by eigenvalue) of the negative Laplacian on a 'triadic Koch snowflake' with zero Neumann boundary conditions (normal derivatives). They represent the harmonics, ordered by frequency of vibration, of a surface whose boundary is a level-5 approximation to a fractal curve with fractal dimension log(4)/log(3) -- about 1.26. Note the 60-degree, 120-degree, and/or 180-degree symmetries and anti-symmetries. The yellow regions, representing nodal lines, are defined by contour values in the range [-.01,.01]. The other regions are associated with contour intervals of length .125. The corresponding eigenvalues are shown in parentheses

The following images are contour plots of the first 50 eigenfunctions (ordered by eigenvalue) of the negative Laplacian on a 'square Koch snowflake' with zero Dirichlet boundary conditions. They represent the harmonics, ordered by frequency of vibration, of a drumhead whose boundary is a level-4 approximation to a fractal curve with fractal dimension 1.5. Note the 90-degree and/or 180-degree symmetries and anti-symmetries. The yellow regions, representing nodal lines, are defined by contour values in the range [-.01,.01]. The other regions are associated with contour intervals of length .125.

The following images are contour plots of the first 49 eigenfunctions (ordered by eigenvalue) of the negative Laplacian on a 'square Koch snowflake' with zero Neumann boundary conditions (normal derivatives). They represent the harmonics, ordered by frequency of vibration, of a surface whose boundary is a level-4 approximation to a fractal curve with fractal dimension 1.5. Note the 90-degree and/or 180-degree symmetries and anti-symmetries. The yellow regions, representing nodal lines, are defined by contour values in the range [-.01,.01]. The other regions are associated with contour intervals of length .125.

The following movie simulates the evolution of the induced magnetic field in a superconducting film dimensioned 30 by 30 (in units of penetration depth) with no external field applied. The Ginzburg- Landau parameter is \kappa = Sqrt(0.5), and the initial configuration consists of a pair of degree-2 vortices and a pair of anti-vortices.