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

Figure 4

Snapshots at the end of the simulation indicate intricate distributions of defectors. The leftmost column presents snapshots of the final generation from runs in which , while the middle column and rightmost column present snapshots from runs in which and , respectively. Panels (a)–(c) present runs in which . Panels (d)–(f) present runs in which and panels (g)–(i) present runs in which . Panels (j)–(l) display the final snapshot of a run when , whereas panels (j)–(l) present the final snapshot for runs in which . The supplementary materials provide complete animations of these and other simulation runs. The panels of Figure 4 show that when cooperators’ expand from their initial allocation at the prime-number locations of Ulam’s spiral, simulations terminate in intricate persistent or oscillating states.