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A271807
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 403", based on the 5-celled von Neumann neighborhood.
4
1, 5, 9, 28, 17, 96, 45, 156, 49, 293, 108, 385, 96, 597, 204, 641, 225, 973, 296, 1097, 329, 1393, 465, 1608, 441, 1893, 633, 2128, 665, 2604, 725, 2913, 756, 3401, 917, 3652, 1105, 4193, 1249, 4636, 1281, 5100, 1481, 5613, 1608, 6165, 1700, 6461, 1825
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=403; 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: A077915 A222357 A271685 * A272287 A272315 A301747
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 14 2016
STATUS
approved