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A289094 Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by "Rule 542", based on the 5-celled von Neumann neighborhood. 4
1, 1, 3, 1, 5, 3, 13, 7, 29, 15, 37, 19, 101, 39, 133, 31, 461, 43, 689, 107, 1725, 139, 2217, 475, 7593, 643, 10241, 1095, 28209, 3879, 33937, 5523, 117973, 13823, 176333, 17655, 428989, 50055, 579997, 75207, 1951453, 219783, 2638213, 358983, 7203309 (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 = 542; 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. A289092, A289093, A289095.

Sequence in context: A289360 A290212 A289891 * A171382 A002323 A294640

Adjacent sequences:  A289091 A289092 A289093 * A289095 A289096 A289097

KEYWORD

nonn,easy

AUTHOR

Robert Price, Jun 23 2017

STATUS

approved

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Last modified November 15 11:35 EST 2018. Contains 317238 sequences. (Running on oeis4.)