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A272539
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 491", based on the 5-celled von Neumann neighborhood.
4
1, 5, 13, 32, 41, 76, 77, 164, 137, 240, 173, 428, 249, 520, 317, 800, 405, 892, 525, 1248, 589, 1408, 733, 1824, 837, 2012, 1025, 2484, 1141, 2700, 1329, 3276, 1465, 3512, 1681, 4172, 1825, 4424, 2089, 5164, 2225, 5456, 2525, 6264, 2673, 6592, 2997, 7464
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=491; 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: A066688 A046789 A271902 * A066184 A231799 A146924
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 02 2016
STATUS
approved