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A273022
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 577", based on the 5-celled von Neumann neighborhood.
4
1, 4, 17, 25, 52, 73, 113, 120, 213, 213, 300, 285, 480, 485, 541, 564, 745, 777, 908, 921, 1184, 1204, 1337, 1333, 1684, 1677, 1877, 1912, 2241, 2225, 2389, 2597, 2800, 2893, 3185, 3108, 3733, 3621, 3808, 4085, 4573, 4340, 4757, 4969, 5400, 5473, 5500, 5760
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=577; 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: A281464 A192197 A009226 * A273119 A302618 A171227
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 13 2016
STATUS
approved