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 A279873 Binary 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 211", based on the 5-celled von Neumann neighborhood. 4
 1, 1, 101, 111, 10000, 10111, 1010100, 1111101, 100000001, 101111111, 10101000000, 11111011111, 1000000000000, 1011111111111, 101010000000000, 111110111111111, 10000000000000000, 10111111111111111, 1010100000000000000, 1111101111111111111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Initialized with a single black (ON) cell at stage zero. REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 170. LINKS Robert Price, Table of n, a(n) for n = 0..126 Robert Price, Diagrams of first 20 stages N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton S. Wolfram, A New Kind of Science Wolfram Research, Wolfram Atlas of Simple Programs FORMULA Conjectures from Colin Barker, Dec 22 2016: (Start) a(n) = a(n-2) + 10000*a(n-4) - 10000*a(n-6) for n>10. G.f.: (1 +x +100*x^2 +110*x^3 -101*x^4 +100*x^6 +990*x^7 -99*x^8 +10*x^9 -x^10 -10000*x^12 +10000*x^14) / ((1 -x)*(1 +x)*(1 -10*x)*(1 +10*x)*(1 +100*x^2)). (End) MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 211; 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]], 10], {i, 1, stages - 1}] CROSSREFS Cf. A279874, A279875, A279876. Sequence in context: A116642 A283590 A279173 * A342040 A290413 A288904 Adjacent sequences: A279870 A279871 A279872 * A279874 A279875 A279876 KEYWORD nonn,easy AUTHOR Robert Price, Dec 21 2016 STATUS approved

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Last modified March 21 08:05 EDT 2023. Contains 361393 sequences. (Running on oeis4.)