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 A357952 Maximum period of a totalistic cellular automaton on a connected graph with n nodes (counting the state of the updated node itself). 2
 2, 2, 4, 6, 8, 18, 42, 112 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Each node can be in one of two states, ON or OFF. The automaton is totalistic, meaning that the state of a node in the next generation depends only on the number of ON-nodes among its neighbors and itself. Since there are finitely many states of the automaton, it will eventually enter a cycle. a(n) is the maximum of the length of that cycle, over all connected graphs with n nodes, all totalistic updating rules, and all initial states. LINKS Table of n, a(n) for n=1..8. The House of Graphs, Graph 21244. Eric Weisstein's World of Mathematics, Spider Graph. Eric Weisstein's World of Mathematics, Totalistic Cellular Automaton. Wikipedia, Cellular automaton. FORMULA a(n) <= A357951(n). EXAMPLE Examples of optimal automata: (The updating rule is given as a set of integers, specifying how many of the neighbors of a node and the node itself must be ON for the node to be ON in the next generation.) n = 1: Path graph; rule {0}; any initial state. n = 2: Path graph; rule {0}; both nodes equal. n = 3: Path graph; rule {1}; one of the end nodes ON. n = 4: Path graph; rule {0,2}; one node ON. n = 5: Spider graph with two legs of length 1 and one leg of length 2; rule {1}; one of the end nodes of the short legs ON. n = 6: 2 X 3 grid with an additional diagonal edge; rule {0,1,3,5}; one degree 2 node (with neighbors of degree 2 and 3) ON. n = 7: Graph 21244 in House of Graphs ('F@Unw' in graph6 format); rule {0,2,4,5,6}; one node of degree 3 and the node of degree 6 ON. n = 8: Graph 'G?Dlvw' in graph6 format; rule {0,2,4}; one of the degree 4 nodes adjacent to the degree 6 node ON. CROSSREFS Cf. A357951, A357953. Sequence in context: A269298 A153964 A001010 * A091966 A231187 A055529 Adjacent sequences: A357949 A357950 A357951 * A357953 A357954 A357955 KEYWORD nonn,more,hard AUTHOR Pontus von Brömssen, Oct 22 2022 STATUS approved

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Last modified June 15 16:55 EDT 2024. Contains 373410 sequences. (Running on oeis4.)