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A271258 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 324", based on the 5-celled von Neumann neighborhood.

%I A271258 #9 Feb 16 2025 08:33:32
%S A271258 3,1,7,-4,16,1,15,-7,11,-4,48,-11,23,21,55,-39,27,-23,63,13,71,21,75,
%T A271258 -31,51,-3,107,5,51,37,123,-23,-29,57,95,25,115,17,187,-39,-5,-11,155,
%U A271258 73,83,73,147,-19,39,-11,203,13,147,21,219,-35,95,13,219,41
%N A271258 First differences of number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 324", based on the 5-celled von Neumann neighborhood.
%C A271258 Initialized with a single black (ON) cell at stage zero.
%D A271258 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
%H A271258 Robert Price, <a href="/A271258/b271258.txt">Table of n, a(n) for n = 0..127</a>
%H A271258 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 [math.CO], 2015
%H A271258 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A271258 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A271258 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A271258 <a href="https://oeis.org/wiki/Index_to_2D_5-Neighbor_Cellular_Automata">Index to 2D 5-Neighbor Cellular Automata</a>
%H A271258 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%t A271258 CAStep[rule_,a_]:=Map[rule[[10-#]]&,ListConvolve[{{0,2,0},{2,1,2},{0,2,0}},a,2],{2}];
%t A271258 code=324; stages=128;
%t A271258 rule=IntegerDigits[code,2,10];
%t A271258 g=2*stages+1; (* Maximum size of grid *)
%t A271258 a=PadLeft[{{1}},{g,g},0,Floor[{g,g}/2]]; (* Initial ON cell on grid *)
%t A271258 ca=a;
%t A271258 ca=Table[ca=CAStep[rule,ca],{n,1,stages+1}];
%t A271258 PrependTo[ca,a];
%t A271258 (* Trim full grid to reflect growth by one cell at each stage *)
%t A271258 k=(Length[ca[[1]]]+1)/2;
%t A271258 ca=Table[Table[Part[ca[[n]][[j]],Range[k+1-n,k-1+n]],{j,k+1-n,k-1+n}],{n,1,k}];
%t A271258 on=Map[Function[Apply[Plus,Flatten[#1]]],ca] (* Count ON cells at each stage *)
%t A271258 Table[on[[i+1]]-on[[i]],{i,1,Length[on]-1}] (* Difference at each stage *)
%Y A271258 Cf. A246316.
%K A271258 sign,easy
%O A271258 0,1
%A A271258 _Robert Price_, Apr 02 2016