Abstract
The behavior of hypercycle spirals in a two-dimensional cellular automaton model is analyzed. Each spiral can be approximated by an Archimedean spiral with center, width, and phase change according to Brownian motion. A barrier exists between two spirals if the phase synchronization hypothesis is taken into account, and the occurrence rate of pair decay (simultaneous disappearance of two spirals) can be explained through a random walk simulation with the barrier. Simulation experiments show that adjacent species violation is necessary to create new spirals. A hypercycle system can live for a long time if spirals in the system are somewhat unstable, since new spirals cannot emerge when existing spirals are too stable.
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