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A270689
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 195", based on the 5-celled von Neumann neighborhood.
4
1, 5, 5, 33, 13, 93, 25, 161, 53, 285, 65, 417, 93, 589, 109, 729, 161, 1029, 117, 1305, 69, 1681, 161, 1833, 305, 2153, 317, 2453, 393, 2885, 389, 3137, 513, 3697, 401, 4329, 357, 4817, 537, 5253, 581, 5833, 697, 6377, 693, 7005, 841, 7405, 925, 8373, 713
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=195; 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: A259264 A259265 A270221 * A270278 A270725 A317812
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 21 2016
STATUS
approved