The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A282482 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 478", based on the 5-celled von Neumann neighborhood. 4
 1, 11, 110, 1111, 11000, 111110, 1100011, 11111110, 110000011, 1111101110, 11000111011, 111111101110, 1100000111011, 11111011101110, 110001110111011, 1111111011101110, 11000001110111011, 111110111011101110, 1100011101110111011, 11111110111011101110 (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 Index entries for sequences related to cellular automata Index to 2D 5-Neighbor Cellular Automata Index to Elementary Cellular Automata Robert Price, Diagrams of first 20 stages FORMULA Conjectures from Colin Barker, Feb 18 2017: (Start) a(n) = a(n-2) + 10000*a(n-4) - 10000*a(n-6) for n>6. G.f.: (1 + 11*x + 109*x^2 + 1100*x^3 + 890*x^4 - x^5 - 989*x^6 + 1000*x^10) / ((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 = 478; 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. A282483, A282484, A282485. Sequence in context: A282006 A280099 A282385 * A286205 A286500 A287099 Adjacent sequences: A282479 A282480 A282481 * A282483 A282484 A282485 KEYWORD nonn,easy AUTHOR Robert Price, Feb 16 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 19 03:10 EDT 2024. Contains 373492 sequences. (Running on oeis4.)