The 4-color FCA on square lattice Ζ^2
The κ-color Firefly Cellular Automaton (FCA) is a discrete model for κ-state pulse-coupled oscillators. While the FCA on lattices for any κ≠4 exhibit local sprials, the 4-color instance on square lattice shows clustering via interacting incomplete spirals.
The 64-state adaptive 4-coupling on uniform spanning tree of Moore lattice
The 4-coupling is a continuum extension of the 4-color FCA. The adaptive 4-coupling is a clock synchronization algorithm based on the 4-coupling, which is able to synchronizes arbitrary initial joint configuration on any trees. If we take a uniform spanning tree of the underlying lattice, the system tries to form spirals but none are completed by topological restriction.