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A283916 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 777", based on the 5-celled von Neumann neighborhood. 4
1, 0, 1, 0, 7, 7, 21, 8, 97, 76, 269, 76, 1805, 1644, 5725, 3604, 27201, 20500, 67265, 21204, 467433, 393472, 1464445, 924444, 6971221, 5255552, 17216949, 5405680, 119556629, 100860096, 375016085, 236454912, 1784410613, 1346036016, 4406938645, 1380720960 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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 = 777; 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. A283914, A283915, A283917.

Sequence in context: A339722 A341833 A253071 * A146804 A147056 A146631

Adjacent sequences:  A283913 A283914 A283915 * A283917 A283918 A283919

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 17 2017

STATUS

approved

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Last modified May 18 14:41 EDT 2022. Contains 353816 sequences. (Running on oeis4.)