login
A270628
Partial sums of the number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 181", based on the 5-celled von Neumann neighborhood.
1
1, 9, 13, 57, 66, 174, 195, 399, 431, 764, 800, 1313, 1349, 2034, 2102, 2983, 3103, 4248, 4316, 5793, 5893, 7650, 7826, 9915, 10103, 12556, 12760, 15697, 15889, 19146, 19450, 23187, 23475, 27812, 28128, 32789, 33309, 38486, 39002, 44951, 45287, 51940, 52404
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=181; 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}];
on=Map[Function[Apply[Plus, Flatten[#1]]], ca] (* Count ON cells at each stage *)
Table[Total[Part[on, Range[1, i]]], {i, 1, Length[on]}] (* Sum at each stage *)
CROSSREFS
Cf. A270626.
Sequence in context: A323797 A270319 A270331 * A270679 A270903 A270936
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 20 2016
STATUS
approved