[seqfan] Re: No loop in view?

[Brad Klee]

Hi Eric,

Define {A,B} two edge-overlap tiles along one dimension, with an
integer shift,

A=101,     B =11,      AB=1011,        BA=1101.

If you chop the first four terms and transform to {A,B} notation,

11010111....
BAABB...

then the letter sequence is the first column of a Post tag system:

Delete:1, Axiom: BA, Rule: A->BBA, B->A
===================================
BA
AA
ABBA
BBABBA
BABBAA...

A slightly simplified example is:

Delete:1, Axiom: A, Rule: A->BA, B->A
===================================
A
BA
AA
ABA
BABA
ABAA
BAABA...

With first column A003849.

I have not studied tag systems in detail, but will guess that the
condition for periodic output is probably much more strict than
for aperiodic output. Analogy with Fibonacci strongly suggests
no looping for your sequence.

Cheers,

Brad

See also: http://mathworld.wolfram.com/TagSystem.html


On Fri, Feb 22, 2019 at 1:58 PM Éric Angelini <bk263401 at skynet.be> wrote:
> Does someone have an idea about the sequence entering at some point
> in a loop -- or never?