Monte Carlo simulation of the color switching dynamics is performed on a two-dimensional trivalent cellular network based on the steady state pattern of a soap froth experiment. An economic interpretation is made on the association of cells to a particular choice of color as representative agents for a particular company. The evolution of color patterns on static cellular network is then interpreted as a manifestation of the competition and cooperation between companies. Different models such as Ising model, length dependent Ising model and vertex model are constructed for different color switching dynamics. In these models we all find existence of phases corresponding to dominant color, as function of the noise level as well as the strength ratio of different color interaction. By anal...[ Read more ]

Monte Carlo simulation of the color switching dynamics is performed on a two-dimensional trivalent cellular network based on the steady state pattern of a soap froth experiment. An economic interpretation is made on the association of cells to a particular choice of color as representative agents for a particular company. The evolution of color patterns on static cellular network is then interpreted as a manifestation of the competition and cooperation between companies. Different models such as Ising model, length dependent Ising model and vertex model are constructed for different color switching dynamics. In these models we all find existence of phases corresponding to dominant color, as function of the noise level as well as the strength ratio of different color interaction. By analyzing the interior bubble distribution function, we can characterize two phases, one with random small cluster and the other with major cluster that percolate the entire froth.