A real Cayley graph, not a toy chain: pick a cyclic group ℤn and a generating set S, and its adjacency matrix becomes the walk Hamiltonian for a continuous-time quantum walk. Every gap between eigenvalues of that graph is a frequency — this is the graph's spectrum, made visible.
This is exactly a continuous-time quantum walk on Cay(ℤn, S): H is the graph's adjacency matrix, and |ψi(t)|² is the same mixing signature used in WalkBasedLayout. No dissipation, so the spectral lines above stay perfectly sharp. Transition strengths use a uniform coupling between every vertex pair — a simplification for the picture, not derived from the graph edges themselves.