Diamond Cubic - Greg Egan

Diamond Cubic

This picture by Greg Egan shows the pattern of carbon atoms in a diamond, called the diamond cubic. Each atom is bonded to four neighbors. This pattern is found not just in carbon but also other elements in the same column of the periodic table: silicon, germanium, and tin.

Weierstrass Elliptic Function (Zoomed Out) - David J. Chudzicki

Weierstrass Elliptic Function

The Weierstrass elliptic function is built up as a sum of terms, one for each point in a lattice in the complex plane. Each term has a pole at one lattice point. The picture here shows the very first term, namely $1/z^2$. That’s why it’s bright in the middle and the colors go twice around the color wheel as you go around. If you continue reading, you’ll see a movie made by David Chudzicki where further terms are added one at a time!

Tübingen Tiling - Greg Egan

Tübingen Tiling

A systematic way to generate quasiperiodic tilings of the plane is to take a lattice in higher dimensions and slice it at a funny angle. Greg Egan has created an applet that generates quasiperiodic tilings by projecting selected triangles from an $n$-dimensional lattice called the $\mathrm{A}_n$ lattice onto a plane. This particular picture comes from the $\mathrm{A}_4$ lattice.