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A278859 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 105", based on the 5-celled von Neumann neighborhood. 4
1, 0, 3, 8, 1, 56, 15, 226, 8, 1007, 2, 4080, 55, 16336, 159, 65204, 151, 261876, 23, 1048180, 983, 4192260, 479, 16775492, 3447, 67101776, 2835, 268428154, 14672, 1073740559, 47204, 4294883375, 14436, 17179867263, 47212, 68719392871, 14450, 274877773932 (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

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=105; 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. A278719, A278739, A278863.

Sequence in context: A118357 A278866 A281287 * A281412 A281306 A281416

Adjacent sequences:  A278856 A278857 A278858 * A278860 A278861 A278862

KEYWORD

nonn,easy

AUTHOR

Robert Price, Nov 30 2016

STATUS

approved

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Last modified September 26 05:07 EDT 2021. Contains 347664 sequences. (Running on oeis4.)