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 A280137 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 237", based on the 5-celled von Neumann neighborhood. 4
 1, 10, 10, 1100, 111, 111110, 10, 11111100, 1111, 1111111000, 1111, 111111111110, 10010, 11111111101100, 101111, 1111111111101010, 10100000, 111111111110011111, 11110000, 11111111111110011111, 111110000, 1111111111111111011111, 1011000 (list; graph; refs; listen; history; text; internal format)
 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. LINKS Robert Price, Table of n, a(n) for n = 0..126 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 Robert Price, Diagrams of first 20 stages MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 237; 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. A280138, A280139, A280140. Sequence in context: A279822 A279959 A279597 * A279502 A279992 A287949 Adjacent sequences:  A280134 A280135 A280136 * A280138 A280139 A280140 KEYWORD nonn,easy AUTHOR Robert Price, Dec 26 2016 STATUS approved

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Last modified June 2 08:00 EDT 2020. Contains 334767 sequences. (Running on oeis4.)