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A279470 Decimal 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 157", based on the 5-celled von Neumann neighborhood. 4
1, 2, 2, 12, 5, 58, 8, 243, 22, 1006, 42, 4036, 81, 16302, 138, 65332, 369, 261854, 722, 1047788, 1453, 4193246, 2642, 16773388, 5229, 67101182, 11522, 268422392, 20111, 1073711992, 41803, 4294908838, 97934, 17179755306, 179088, 68719308495, 293624 (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

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 = 157; 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]], 2], {i, 1, stages - 1}]

CROSSREFS

Cf. A279468, A279469, A279471.

Sequence in context: A279718 A279671 A279179 * A013605 A073768 A278534

Adjacent sequences:  A279467 A279468 A279469 * A279471 A279472 A279473

KEYWORD

nonn,easy

AUTHOR

Robert Price, Dec 12 2016

STATUS

approved

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Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)