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A282076 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 421", based on the 5-celled von Neumann neighborhood. 4
1, 1, 6, 3, 28, 31, 112, 15, 368, 191, 1856, 1279, 5888, 3839, 29696, 28415, 118016, 99327, 474112, 270335, 1323008, 544767, 7385088, 6307839, 29786112, 18661375, 88686592, 46333951, 410320896, 430637055, 1841561600, 1519583231, 7356350464, 6057885695 (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

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 = 421; 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. A282073, A282074, A282075.

Sequence in context: A282303 A286166 A286174 * A282553 A163913 A022666

Adjacent sequences:  A282073 A282074 A282075 * A282077 A282078 A282079

KEYWORD

nonn,easy

AUTHOR

Robert Price, Feb 05 2017

STATUS

approved

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Last modified March 28 04:44 EDT 2020. Contains 333073 sequences. (Running on oeis4.)