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 A284028 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 790", based on the 5-celled von Neumann neighborhood. 3
 1, 11, 101, 1111, 10111, 111011, 1010101, 11111111, 101111111, 1110111111, 10101011111, 111111101111, 1011111010111, 11101110111011, 101010101010101, 1111111111111111, 10111111111111111, 111011111111111111, 1010101111111111111, 11111110111111111111 (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 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 MATHEMATICA CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code = 790; 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. A284029, A284031. Sequence in context: A209930 A203304 A283906 * A284407 A284479 A290661 Adjacent sequences: A284025 A284026 A284027 * A284029 A284030 A284031 KEYWORD nonn,easy AUTHOR Robert Price, Mar 18 2017 STATUS approved

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Last modified February 6 18:02 EST 2023. Contains 360111 sequences. (Running on oeis4.)