Dynamical properties of threshold automata with nearest-neighbor interactions on a regular lattice

It is demonstrated that threshold automata with quasirandom nearest-neighbor interactions on a regular two-dimensional lattice exhibit, by far, more frozen behavior than their infinite-range counterparts. Systems with units residing on a honeycomb lattice strictly remain in an ordered condition, whereas for the square lattice based on five nearest-neighbor interactions, a phase transition from ordered to chaotic behavior is detected. After only a few time steps, a Hebbian-like self-organization procedure applied to the square lattice network leads to exclusively nonchaotic behavior.<>