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A272149
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 435", based on the 5-celled von Neumann neighborhood.
4
1, 5, 13, 36, 33, 92, 65, 185, 76, 289, 136, 421, 221, 565, 260, 785, 293, 1020, 369, 1244, 529, 1504, 605, 1804, 673, 2104, 857, 2420, 1009, 2844, 1257, 3329, 1348, 3677, 1313, 4264, 1433, 4612, 1817, 5204, 1953, 5636, 2305, 6124, 2389, 6764, 2741, 7469
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=435; 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: A229924 A264080 A290588 * A272560 A266102 A332599
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 21 2016
STATUS
approved