Turns out using 4 transpositions to generate S_5 gives a much more symmetric looking Cayley Graph.

Cayley graph of S_5 embedded in R^4 using 4 of the eigenvectors of the graph Laplacian. 4D rotation projected into 3D.

Incorporating "deeper" math in my creative coding endeavors. This takes a Cayley Graph for the symmetric group with the minimal 2 element generating set consisting of one transposition and one cycle. Draws graph using eigenvectors pairs of graph Laplacian to get vertex x and ys.

70% me, 30% ChatGPT

Prompt: grid based graphic design.

Complement of a stage 2 Menger sponge. 3D perspective drawing completely coded by hand.