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A271594
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 389", based on the 5-celled von Neumann neighborhood.
4
1, 8, 5, 40, 17, 104, 17, 196, 45, 300, 49, 456, 69, 608, 77, 824, 101, 1056, 149, 1260, 213, 1556, 201, 1868, 229, 2252, 301, 2512, 421, 2920, 393, 3404, 377, 3828, 593, 4168, 629, 4816, 681, 5336, 693, 5924, 777, 6468, 905, 7016, 989, 7652, 897, 8516, 1073
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=389; 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: A196123 A196120 A213841 * A272273 A272049 A272350
KEYWORD
nonn,easy,changed
AUTHOR
Robert Price, Apr 10 2016
STATUS
approved