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A278873 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 99", based on the 5-celled von Neumann neighborhood. 4
1, 2, 4, 15, 4, 59, 0, 239, 0, 767, 1088, 4095, 320, 15039, 1280, 64511, 16640, 260863, 82944, 961535, 86016, 2797567, 5586944, 11186175, 22364160, 44761087, 89407488, 178978815, 357842944, 716095487, 1430323200, 2863661055, 5725290496, 11458772991 (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

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=99; 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. A278870, A278871, A278872.

Sequence in context: A347790 A199931 A163361 * A278901 A278918 A279025

Adjacent sequences:  A278870 A278871 A278872 * A278874 A278875 A278876

KEYWORD

nonn,easy

AUTHOR

Robert Price, Nov 29 2016

STATUS

approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)