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A278424 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 41", based on the 5-celled von Neumann neighborhood. 4
1, 0, 4, 3, 20, 3, 112, 47, 272, 143, 1088, 575, 4416, 2111, 22272, 2815, 114944, 47359, 283648, 132095, 1168384, 558079, 4485120, 2273279, 22024192, 757759, 130367488, 44056575, 274546688, 237518847, 1158086656, 552271871, 4785766400, 2822307839 (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=41; 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. A278421, A278422, A278423.

Sequence in context: A178417 A178628 A167479 * A278662 A220861 A270797

Adjacent sequences:  A278421 A278422 A278423 * A278425 A278426 A278427

KEYWORD

nonn,easy

AUTHOR

Robert Price, Nov 21 2016

STATUS

approved

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Last modified November 30 02:42 EST 2020. Contains 338781 sequences. (Running on oeis4.)