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 A278898 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 107", based on the 5-celled von Neumann neighborhood. 4
 1, 1, 1, 1111, 100, 110111, 0, 11110111, 10100, 1111010111, 10100, 111111110111, 1010100, 11111101010111, 1010100, 1111111111010111, 101010100, 111111110101010111, 101010100, 11111111111101010111, 10101010100, 1111111111010101010111, 10101010100 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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 Index entries for sequences related to cellular automata Index to 2D 5-Neighbor Cellular Automata Index to Elementary Cellular Automata FORMULA Conjectures from Colin Barker, Nov 30 2016: (Start) a(n) = 101*a(n-2) - 10100*a(n-6) + 10000*a(n-8) for n>15. G.f.: (1 +x -100*x^2 +1010*x^3 -x^4 -2100*x^5 -1000*x^7 +10200*x^8 +100000*x^9 -10000*x^10 +100000*x^11 -1010000*x^12 -10100000*x^13 +1000000*x^14 +10000000*x^15) / ((1 -x)*(1 +x)*(1 -10*x)*(1 +10*x)*(1 -10*x^2)*(1 +10*x^2)). (End) MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=107; 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. A278899, A278900, A278901. Sequence in context: A277927 A086887 A278870 * A278915 A278980 A290848 Adjacent sequences: A278895 A278896 A278897 * A278899 A278900 A278901 KEYWORD nonn,easy AUTHOR Robert Price, Nov 30 2016 STATUS approved

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Last modified December 4 14:29 EST 2023. Contains 367563 sequences. (Running on oeis4.)