|
|
A105220
|
|
Trajectory of 1 under the morphism 1->{1,2,1}, 2->{2,2,2}.
|
|
4
|
|
|
1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Dekking substitution for the Cantor set: characteristic polynomial = x^2 - 5*x + 6 of matrix [2, 0; 1, 3].
This substitution is useful for computing the devil's staircase by bb=aa/. 1->1/3/. 2->0 /. 3->0; ListPlot[FoldList[Plus, 0, bb], PlotRange -> All, PlotJoined -> True, Axes ->False];
The Wikipedia article on L-system Example 3 is "Cantor dust" given by the axiom: A and rules: A -> ABA, B -> BBB. This is isomorphic to the system given in the sequence name. - Michael Somos, Jan 12 2015
|
|
LINKS
|
F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no. 1, 1982, page 99, section 4.15
Wikipedia, L-system Example 3: Cantor dust
|
|
FORMULA
|
a(n) = 2 if the ternary expansion of n contains the digit 1, otherwise a(n) = 1. - Joerg Arndt, Aug 24 2019
|
|
MATHEMATICA
|
Flatten[ Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {2, 2, 2}} &], {1}, 5]]
|
|
PROG
|
(PARI)
A088917(n) = { while(n, if(n%3==1, return(0), n\=3)); (1); }; \\ Originally from A005823
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|