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A278593 Binary 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 51", based on the 5-celled von Neumann neighborhood. 4
1, 10, 100, 1011, 10000, 101111, 1000000, 10111111, 100000000, 1011111111, 10000000000, 101111111111, 1000100000000, 10101011111111, 101010000000000, 1010101111111111, 10101000000000000, 101010111111111111, 1010100000000000000, 10101011111111111111 (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=51; 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]], 10], {i, 1, stages-1}]

CROSSREFS

Cf. A278592, A278594, A278595.

Sequence in context: A283249 A278344 A277865 * A283132 A283214 A283291

Adjacent sequences:  A278590 A278591 A278592 * A278594 A278595 A278596

KEYWORD

nonn,easy

AUTHOR

Robert Price, Nov 23 2016

STATUS

approved

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Last modified October 26 02:14 EDT 2021. Contains 348256 sequences. (Running on oeis4.)