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A270938
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 222", based on the 5-celled von Neumann neighborhood.
4
1, 5, 12, 20, 32, 32, 72, 60, 112, 88, 164, 144, 236, 184, 292, 260, 392, 336, 452, 464, 584, 548, 616, 652, 720, 676, 988, 812, 1076, 1016, 1120, 1148, 1372, 1296, 1508, 1500, 1848, 1636, 1872, 1804, 2068, 2036, 2428, 2012, 2540, 2348, 2900, 2436, 3036
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=222; 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: A086570 A366101 A270333 * A270079 A266937 A270214
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 26 2016
STATUS
approved