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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A279991 Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 225", based on the 5-celled von Neumann neighborhood. 4
1, 0, 7, 0, 23, 8, 95, 48, 375, 232, 1183, 1232, 151, 12680, 4703, 40112, 43127, 22248, 437663, 350928, 700567, 1404808, 2809439, 5605552, 11227255, 22449896, 44914079, 89795280, 179372183, 359202696, 718605919, 360904880, 7169478775, 5738573544, 11506226591 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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
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
MATHEMATICA
CAStep[rule_, a_] := Map[rule[[10 - #]] &, ListConvolve[{{0, 2, 0}, {2, 1, 2}, {0, 2, 0}}, a, 2], {2}];
code = 225; 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[i, 2 * i - 1]], 2], {i , 1, stages - 1}]
CROSSREFS
Sequence in context: A282071 A064854 A199917 * A282489 A281672 A281846
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 24 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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 3 10:04 EST 2024. Contains 370510 sequences. (Running on oeis4.)