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A273750
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 926", based on the 5-celled von Neumann neighborhood.
3
1, 5, 13, 21, 37, 45, 77, 85, 117, 125, 189, 197, 229, 269, 365, 341, 405, 413, 541, 549, 581, 685, 845, 757, 885, 893, 1021, 1157, 1189, 1293, 1581, 1365, 1493, 1501, 1757, 1765, 1797, 2029, 2317, 2101, 2357, 2365, 2493, 2885, 2917, 3021, 3565, 3093, 3221
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=926; 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: A316357 A252296 A273569 * A191116 A166051 A160170
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 30 2016
STATUS
approved