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A283046 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 563", based on the 5-celled von Neumann neighborhood. 4
1, 1, 1, 1, 5, 5, 21, 29, 73, 73, 329, 457, 1161, 1193, 5289, 7337, 18665, 19017, 84553, 117321, 298569, 304201, 1353033, 1877833, 4776521, 4868681, 21645897, 30034505, 76433993, 77875785, 346376777, 480758345, 1222871625, 1246308937, 5541276233, 7688759881 (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 = 563; 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. A283044, A283045, A283047.

Sequence in context: A052992 A280147 A279666 * A147254 A241864 A243121

Adjacent sequences:  A283043 A283044 A283045 * A283047 A283048 A283049

KEYWORD

nonn,easy

AUTHOR

Robert Price, Feb 27 2017

STATUS

approved

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Last modified February 21 04:55 EST 2020. Contains 332086 sequences. (Running on oeis4.)