ABSTRACT
This chapter includes the analytic approximation of macroscopic dynamics, systems of coupled selectors, and group meeting problems in nonlocal cellular automata investigation. It introduces some model systems which are high-dimensional, fully discretized, synchronous, and uniform dynamical systems with nonlocal connections. Besides the dynamical rule, the wiring diagram of a network also plays an important role in determining the dynamics. It could happen that with the same rule, some wiring diagrams lead to one type of dynamics, while other wiring diagrams lead to another. The chapter talks about dynamics of a nonlocal cellular automaton rule, there is an implication that almost all wiring diagrams lead to the same dynamics. The wiring diagram dictates where to take inputs for each component. In some sense, it determines the direction of information flows. Obviously wiring diagrams with different topological structures will transmit information in different ways, and dynamical behaviours can also be different.
