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A270152
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 97", based on the 5-celled von Neumann neighborhood.
4
1, 4, 9, 32, 13, 84, 21, 172, 25, 272, 49, 408, 81, 572, 73, 804, 129, 944, 153, 1232, 164, 1517, 144, 1864, 225, 2060, 237, 2568, 316, 2817, 320, 3209, 372, 3700, 436, 4156, 468, 4604, 536, 5088, 652, 5744, 776, 6164, 704, 6748, 856, 7600, 717, 8068, 836
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=97; 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: A201689 A356650 A270909 * A271305 A270160 A271414
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 12 2016
STATUS
approved