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A270677
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 189", based on the 5-celled von Neumann neighborhood.
4
1, 8, 4, 44, 9, 108, 21, 212, 20, 353, 24, 513, 48, 708, 45, 940, 48, 1201, 64, 1460, 116, 1804, 92, 2096, 188, 2496, 124, 2933, 180, 3389, 188, 3857, 220, 4328, 313, 4836, 325, 5472, 361, 5980, 429, 6648, 525, 7308, 505, 7992, 529, 8688, 605, 9532, 521
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=189; 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: A270317 A270329 A270626 * A270901 A270934 A271004
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 21 2016
STATUS
approved