login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A284349 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 873", based on the 5-celled von Neumann neighborhood. 4
1, 0, 3, 5, 10, 29, 58, 95, 175, 503, 1019, 1525, 3066, 8189, 16382, 24575, 45055, 129023, 262143, 393215, 786431, 2097151, 4194303, 6291455, 11534335, 33030143, 67108863, 100663295, 201326591, 536870911, 1073741823, 1610612735, 2952790015, 8455716863 (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 = 873; 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. A284347, A284348, A284350.

Sequence in context: A003187 A262306 A284301 * A003186 A006826 A000214

Adjacent sequences:  A284346 A284347 A284348 * A284350 A284351 A284352

KEYWORD

nonn,easy

AUTHOR

Robert Price, Mar 25 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 8 23:53 EDT 2021. Contains 343685 sequences. (Running on oeis4.)