Cellular Automata의 창발적 특성을 정성적 및 morphological 분석방법 이해 제4주. Cellular Automata A survey of cellular automata like the “game of life” A.C. de la Torre and H.O. Martin, Physica A, vol. 240, pp. 560~570, 1997 학습목표 Cellular Automata의 창발적 특성을 정성적 및 morphological 분석방법 이해
개요 Game of life (Conway, 1982) Statistical properties & morphology analysis 8 neighboring 2-D lattice (4+4) with simultaneous change From a random distribution until 1000 time steps 0 1 if 3 neighbors 1 0 if less than 2 or more than 3 neighbors If =[f1, f2], Is = [s1, s2] (f1, f2, s1, s2) : game description 예: (3, 3, 2, 3) 내용 (1, 1, 1, 1) ~ (8, 8, 8, 8) : 1296 games after 1000 steps in 100*100 How other games look like for arbitrary intervals of fertility and of survival Density Activity : average between rate of fertility and rate of mortality Mean-field arguments and morphological description
Survey of all games 1296 games for 1000 time steps on 100*100 lattice Initial densities : 0.001, 0.1, 0.3, 0.5 Five runs each 결과 그림 1: 3개 그룹의 density histogram 그림 2: 0이나 1에 가까운 그룹 그림 3: density vs. activity absolute bound, mean field bound
Morphology of some games Ferromagnetic structure (4, 4, 1, 4) : 그림 4 Labyrinth structure (3, 3, 1, 4) : 그림 5 Percolating structure (5, 8, 4, 8) : 그림 6 Combat structure (3, 8, 5, 8) : 그림 7 Cerebral cortex structure (1, 6, 1, 6) : 그림 8
정리 1296 game의 분석 Density and activity Mean-field analysis Rich variety of structures resembling shapes found in nature No game was found with features as fascinating as those of “life”