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First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 630", based on the 5-celled von Neumann neighborhood.
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%I #7 Jul 28 2024 10:59:32

%S 4,4,12,8,16,20,24,36,8,28,20,32,48,16,56,12,148,28,52,4,76,20,112,24,

%T 96,104,24,-36,204,-8,164,32,352,-180,304,-52,200,-24,232,-64,200,36,

%U 188,-32,284,172,-24,260,128,204,128,-108,256,-24,396,-68,172,256

%N First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 630", based on the 5-celled von Neumann neighborhood.

%C Initialized with a single black (ON) cell at stage zero.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.

%H N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168, 2015

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>

%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>

%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>

%t rule=630; stages=300; ca=CellularAutomaton[ {rule,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}}, {{{1}},0}, stages]; (* Start with single black cell *) on=Map[Function[Apply[Plus,Flatten[#1]]],ca]; (* Count ON cells at each stage *) Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}]

%Y Cf. A269523.

%K sign,easy

%O 0,1

%A _Robert Price_, Mar 01 2016