The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A278466 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 49", based on the 5-celled von Neumann neighborhood. 4
 1, 0, 1, 1100, 1, 111100, 1, 11111100, 1001, 1111100000, 1111, 111111100000, 1111, 11111111100100, 1, 1111111111111100, 11001001, 111111111000000000, 11111111, 11111111111001001100, 1, 1111111111111111111100, 1101011001, 111111111111100010000000, 1010111111 (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 MATHEMATICA CAStep[rule_, a_]:=Map[rule[[10-#]]&, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}]; code=49; 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. A278467, A278468, A278469. Sequence in context: A261911 A276708 A277797 * A280973 A260592 A278421 Adjacent sequences: A278463 A278464 A278465 * A278467 A278468 A278469 KEYWORD nonn,easy AUTHOR Robert Price, Nov 22 2016 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 May 30 13:17 EDT 2023. Contains 363050 sequences. (Running on oeis4.)