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A272115
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 430", based on the 5-celled von Neumann neighborhood.
3
1, 5, 8, 21, 24, 37, 44, 85, 96, 101, 116, 149, 168, 197, 228, 341, 400, 357, 420, 405, 472, 453, 532, 597, 696, 645, 756, 789, 912, 933, 1092, 1365, 1648, 1381, 1668, 1429, 1720, 1477, 1780, 1621, 1944, 1669, 2004, 1813, 2160, 1957, 2340, 2389, 2872, 2437
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=430; 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: A246330 A034737 A271156 * A268195 A169705 A138810
KEYWORD
nonn,easy
AUTHOR
Robert Price, Apr 20 2016
STATUS
approved