New Challenges in Cellular Automata Due to Network Geometry—Ferromagnetic Transition Study
Self-organization to ferromagnetic phase transition in cellular automata of spins governed by stochastic majority rule and when topology between spins is changed, is investigated by simulations. Three types of edge rewiring are considered. The algorithm of Watts and Strogatz is applied at each time step to establish a network evolving stochastically (the first network). The preference functions are defined to amplify the role of strongly connected vertices (the second network). Demand to protect graph connectivity provides the third way of edge rewiring. Depending on applied network stochastic, the majority rule leads or does not lead to ferromagnetic transition. The most stable ferro phase is found when a network is similar to the scale-free network. Some discussion on other applications of cellular automata on evolving network is included.