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A273304
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 637", based on the 5-celled von Neumann neighborhood.
4
1, 8, 20, 45, 61, 112, 136, 212, 224, 341, 349, 492, 524, 684, 708, 892, 892, 1140, 1156, 1432, 1448, 1756, 1716, 2112, 2008, 2488, 2336, 2892, 2732, 3376, 3292, 3785, 3441, 4269, 4021, 4789, 4533, 5361, 5105, 5977, 5537, 6545, 6185, 7229, 6853, 7949, 7589
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=637; 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: A273241 A273295 A273266 * A169878 A107816 A361073
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 19 2016
STATUS
approved