Patterns in a PDE on the Koch Snowflake

Two Kock Snowflakes Tile the Plane

Download a pdf of Computing Eigenfunctions on the Kock Snowflake: A New Grid and Symmetry (3,250 KB). This paper has been accepted by the Journal of Computational and Applied Mathematics (JCAM).

The following links are to contour plots of eigenfunctions of the Laplacian on the Kock Snowflake. (The paper has just a handful of these contour plots.)
Eigenfunctions with Dirichlet boundary conditions
Eigenfunctions with Neumann boundary conditions

Download a pdf of Symmetry and Branch Following for a Semilinear Elliptic PDE on a Fractal Region (3,916 KB). This paper has been submitted to the SIAM Journal on Applied Dynamical Systems (SIADS).

The following link has gif files of nonlinear solutions with each of the 22 nontrivial symmetry types. (These figures are found in the "Symmetry and Branch Following" paper, but the gifs take much less time to download than the pdf.)
Nonlinear solutions

The following links are to animations referred to in the paper.
Animations of Figure 7.     Animations of Figure 8b.     Animations of Figure 10.