The final version is here, and the paper is also available as a preprint at the arXiv.

There are two parallel web sites. To switch between static and interactive options come back to this “PDE on Cube Home” page using the link at the top of each page, and click the other option.

static: figures that load quicker, or

interactive: 3D figures
that you can rotate with the mouse.

The “static” and “interactive” links above take you to a page that lists all symmetry types at once. From there you can click a link to a separate page for each of the 99 symmetry types. You can also jump from the page for one symmetry type to the page for another. The “symmetry types” link on the second line of each page takes you to the page with all of the symmetry types.

The page for each symmetry type shows a flag diagram (either static or interactive) for a function with this symmetry type, and possible generic bifurcations with symmetry between these symmetry types. If we have actually found a solution with this symmetry type then a contour map of the solution is shown. (Sadly, the contour maps cannot rotate interactively, only the flag diagrams.)

This web site uses S_{4} to denote the 24-element symmetric group.
The Octahedral group O and the full symmetry group
of the tetrahedron T_{d} are both isomorphic to S_{4}, as indicated in Figure 3 of the
preprint.
Both O and T_{d} are written as S_{4} in the web site.
Similarly, the web site uses A_{4} to denote the 12-element alternating group. Figure 3 in the preprint.

The computations were done using MPQueue,
a package for simplified
parallel computing.
The paper has appeared in print here, and the preprint is
here.

The source code is freely available at our web site.

e-mail: Jim.Swift@nau.edu