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A282268 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 449", based on the 5-celled von Neumann neighborhood. 4
1, 0, 7, 0, 31, 0, 127, 0, 511, 0, 2047, 0, 8191, 0, 31999, 0, 114943, 15360, 445695, 61440, 1573119, 523264, 7868415, 1044480, 29364223, 8187904, 117444607, 32763904, 402657279, 350220288, 1073745151, 463466496, 6442463487, 8124304384, 17230462207 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Initialized with a single black (ON) cell at stage zero.

Similar to A279723 but differing at a(30).

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

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 = 449; 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

Cf. A282265, A282266, A282267, A279723.

Sequence in context: A282492 A335538 A279723 * A279722 A282267 A282298

Adjacent sequences:  A282265 A282266 A282267 * A282269 A282270 A282271

KEYWORD

nonn,easy

AUTHOR

Robert Price, Feb 10 2017

STATUS

approved

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Last modified October 2 04:54 EDT 2022. Contains 357191 sequences. (Running on oeis4.)