Seeding the Spatial Prisoner’s Dilemma with Ulam’s Spiral

Figure 1

Cooperators arranged in Ulam’s spiral grow their population share when and . The figure presents the final proportion of cooperators across values of and small values of to identify critical values of those parameters influencing cooperation. As Figure 1 indicates, cooperators either constitute a dominant final portion of the population (green-to-blue region of the figure) or they go extinct (pink region). Moderate shares of the population, indicated in the color key by yellow, do not appear in simulation results. These findings, displayed in Figure 1, demarcate the narrow parameter range in which cooperation can evolve in the boundary game variant of the spatial PD when cooperators are arranged at the prime-number values of Ulam’s spiral.