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A271195
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 310", based on the 5-celled von Neumann neighborhood.
4
1, 5, 8, 20, 28, 40, 45, 81, 93, 120, 116, 192, 137, 249, 188, 292, 340, 341, 436, 448, 500, 521, 548, 709, 660, 757, 725, 900, 932, 976, 965, 1273, 1080, 1356, 1312, 1512, 1344, 1692, 1529, 1760, 1840, 1973, 1948, 2165, 2237, 2237, 2336, 2524, 2744, 2692
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=310; 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: A143157 A275236 A270022 * A270630 A272217 A084568
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 01 2016
STATUS
approved