So… are those mountains? Yes, or some abstract combination of mountains and waves. Movement on a landscape is a common theme in my research projects. The idea that dynamical behavior is related to the topography of some landscape comes up in physics and quantitative biology (including aspects of evolution). Those landscapes generally live in a high-dimensional space. The mountainscapes, happily, live in 3D — much easier to render!

Two main ingredients went into the splash and banner images for this site: (1) a simple mathematical description of the landscape (altitude as a smooth function of position), and (2) some 3D rendering to create the landscape mesh, apply color, add lighting, etc. I used the Python module NumPy (for the former) and the 3D rendering program Blender (for the latter). In the mini-wiki there's a bit about these and other pieces of software I've found useful.

For those interested, here are the technical highlights of the mountainscape creation process:
$$x,y$$ position, height, and width are specified for each hill/peak
the hills are based on 2D Gaussians or squared oscillatory functions
each peak is a truncated sigmoid curve rotated $$360^{\circ}$$ to give it cylindrical symmetry
the landscape function is evaluated at a regular 2D triangular lattice of points, yielding the 3D mesh surface
parallel light rays from a sun-like point source (infinitely strong and far away) illuminate the scene
the subtle ridges on the peaks in the splash image are due to a bug; I found and fixed the bug, but then realized I liked the effect it produced, so I put it back in! ☺