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A273111
Number of active (ON, black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 589", based on the 5-celled von Neumann neighborhood.
4
1, 8, 20, 41, 61, 93, 129, 180, 208, 268, 321, 413, 433, 592, 592, 773, 797, 885, 1028, 1085, 1233, 1349, 1504, 1661, 1692, 1941, 2052, 2300, 2349, 2549, 2745, 3004, 2952, 3409, 3405, 3729, 3817, 4281, 4237, 4712, 4801, 5049, 5252, 5621, 5756, 6044, 6412
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=589; 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: A272924 A272943 A272995 * A273175 A318071 A308904
KEYWORD
nonn,easy
AUTHOR
Robert Price, May 15 2016
STATUS
approved