{"paper":{"title":"Density decay and growth of correlations in the Game of Life","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"F. Cornu, H.J. Hilhorst","submitted_at":"2018-09-10T12:22:00Z","abstract_excerpt":"We study the Game of Life as a statistical system on an $L\\times L$ square lattice with periodic boundary conditions. Starting from a random initial configuration of density $\\rho_{\\rm in}=0.3$ we investigate the relaxation of the density as well as the growth with time of spatial correlations. The asymptotic density relaxation is exponential with a characteristic time $\\tau_L$ whose system size dependence follows a power law $\\tau_L\\propto L^z$ with $z=1.66\\pm 0.05$ before saturating at large system sizes to a constant $\\tau_\\infty$. The correlation growth is characterized by a time dependent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03266","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}