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A270333
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 158", based on the 5-celled von Neumann neighborhood.
4
1, 5, 12, 20, 32, 32, 64, 52, 104, 60, 152, 108, 200, 176, 268, 236, 328, 260, 452, 292, 520, 388, 656, 480, 784, 516, 908, 648, 1096, 724, 1204, 916, 1240, 1000, 1452, 1088, 1532, 1316, 1792, 1368, 1976, 1636, 2208, 1732, 2280, 2208, 2292, 2272, 2612, 2528
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=158; 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 *)
Total[#, 2] & /@ CellularAutomaton[{158, {2, {{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}}, {1, 1}}, {{{1}}, 0}, {20}] (* JungHwan Min, Mar 16 2016 *)
CROSSREFS
Sequence in context: A326663 A086570 A366101 * A270938 A270079 A266937
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 15 2016
STATUS
approved