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A273972
Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 20", based on the 5-celled von Neumann neighborhood.
4
1, 2, 4, 8, 16, 34, 68, 128, 256, 544, 1088, 2056, 4112, 8738, 17476, 32768, 65536, 139264, 278528, 526336, 1052672, 2236928, 4473856, 8388736, 16777472, 35652128, 71304256, 134744072, 269488144, 572662306, 1145324612, 2147483648, 4294967296, 9126805504
OFFSET
0,2
Initialized with a single black (ON) cell at stage zero.
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170.
FORMULA
a(2*n+2) = 2*a(2*n+1). - Paul Curtz, Nov 16 2016
MATHEMATICA
CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code=20; 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}];
Table[FromDigits[Part[ca[[i]][[i]], Range[1, i]], 2], {i, 1, stages-1}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Nov 09 2016
STATUS
approved

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Last modified September 20 18:47 EDT 2024. Contains 376075 sequences. (Running on oeis4.)