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A273703
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 870", based on the 5-celled von Neumann neighborhood.
4
1, 5, 5, 17, 5, 25, 17, 61, 9, 45, 45, 129, 57, 141, 117, 285, 121, 209, 217, 317, 265, 393, 397, 625, 501, 561, 617, 797, 697, 881, 845, 1097, 933, 1065, 1141, 1269, 1097, 1325, 1361, 1613, 1541, 1677, 1673, 1909, 1945, 2305, 2141, 2357, 2145, 2325, 2365
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=870; 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: A273502 A273606 A273544 * A253065 A294612 A246332
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 28 2016
STATUS
approved