login
A270634
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 185", based on the 5-celled von Neumann neighborhood.
4
1, 4, 9, 32, 33, 92, 65, 176, 53, 316, 113, 432, 189, 548, 284, 801, 300, 1028, 420, 1272, 476, 1488, 672, 1840, 676, 2180, 840, 2488, 976, 2828, 1212, 3320, 1260, 3716, 1424, 4272, 1448, 4656, 1780, 5256, 1932, 5700, 2212, 6284, 2432, 6740, 2816, 7564, 2828
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=185; 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: A053192 A338576 A270618 * A324020 A265645 A005985
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 20 2016
STATUS
approved