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A273557
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 785", based on the 5-celled von Neumann neighborhood.
4
1, 4, 13, 28, 49, 77, 104, 141, 180, 241, 268, 353, 392, 485, 544, 629, 700, 825, 884, 1033, 1104, 1261, 1352, 1501, 1604, 1777, 1868, 2049, 2184, 2341, 2464, 2645, 2780, 3033, 3156, 3433, 3568, 3853, 4008, 4285, 4452, 4753, 4908, 5217, 5416, 5701, 5888
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=785; 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: A056107 A155433 A272746 * A272790 A273564 A155392
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 25 2016
STATUS
approved