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A272834
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 545", based on the 5-celled von Neumann neighborhood.
4
1, 4, 17, 28, 57, 84, 117, 140, 205, 264, 317, 400, 465, 512, 581, 652, 749, 928, 973, 1204, 1313, 1388, 1545, 1672, 1817, 2044, 2093, 2320, 2441, 2484, 2609, 2724, 2969, 3384, 3429, 3832, 4009, 4272, 4477, 4840, 5093, 5344, 5597, 5928, 6145, 6376, 6597
OFFSET
0,2
COMMENTS
Initialized with a single black (ON) cell at stage zero.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=545; stages=128;
rule=IntegerDigits[code, 2, 10];
g=2*stages+1; (* Maximum size of grid *)
a=PadLeft[{{1}}, {g, g}, 0, Floor[{g, g}/2]]; (* Initial ON cell on grid *)
ca=a;
ca=Table[ca=CAStep[rule, ca], {n, 1, stages+1}];
PrependTo[ca, a];
(* Trim full grid to reflect growth by one cell at each stage *)
k=(Length[ca[[1]]]+1)/2;
ca=Table[Table[Part[ca[[n]][[j]], Range[k+1-n, k-1+n]], {j, k+1-n, k-1+n}], {n, 1, k}];
Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
CROSSREFS
Sequence in context: A366210 A335593 A319970 * A273573 A272846 A273610
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 07 2016
STATUS
approved