Figure 2
Two dimensional cellular automata operating between order and chaos behave like excitable membranes in biological cells. A. A two dimensional cellular automaton was constructed with the program CaSim using units with four states, i.e. one open, one closed and two inactive states. Four different rule sets were used to generate the four time series in the figure. The cellular automaton was seeded at R1 by setting two units to the open state and the times series calculated. The configuration of the cellular automata at iterations 0, 1, 25, 50 and 100 are presented in the figure for the four rule sets. The entropy of the rule sets was determined by calculating the probability of each state (Ps) from 10 runs of 1000 iterations. For these calculations 10 percent of the units were set to the open state at R1. Entropy was calculated using the equation: entropy = -∑ Ps ln (Ps). The entropy of each rule set was then expressed as a ratio of the calculated entropy to the maximum entropy (bottom of the figure). The maximum entropy is when all four states have a probability of 0.25. B. The "potentials" generated by the rule sets in A were graphed by plotting the number of open channels versus time. These plots indicate that only the transition rule set produces channel openings that are similar to action potentials in biological membranes.