Spiral-lattice-site animals: an exact enumeration study

Abstract

Spiral-lattice-site animals are studied on a square lattice by exact enumeration methods. The number of animals g_s, their average perimeter t_s and the average radius of gyration R_s are obtained exactly for all s-sited animals up to s=11. We find as s →∞ , g_sλ ^s with λ =2.811± 0.002 t_s~As with A=1.157± 0.020, and R_s~s^ρ with ρ =0.499± 0.030. These results are discussed and comparisons with ordinary and directed lattice animals are made.