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A270716
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 197", based on the 5-celled von Neumann neighborhood.
4
1, 8, 4, 40, 17, 100, 25, 184, 56, 321, 52, 421, 140, 661, 80, 821, 156, 1069, 136, 1277, 292, 1580, 261, 1948, 301, 2184, 341, 2588, 413, 2984, 397, 3476, 525, 3752, 565, 4424, 577, 4912, 629, 5360, 781, 5912, 909, 6396, 869, 7188, 937, 7732, 1197, 8428
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=197; 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: A279635 A213505 A270232 * A270457 A270946 A270282
KEYWORD
nonn,easy
AUTHOR
Robert Price, Mar 22 2016
STATUS
approved