Triple FJS

[alexandre.wajnberg at skynet.be]

Le mardi, 3 mai 2005, à 12:15 Europe/Brussels, Joerg Arndt a écrit :

> * Eric Angelini <keynews.tv at skynet.be> [May 03. 2005 12:19]:
>> Hello SeqFans,
>> I'm working on "Fractal Jump Sequences" for the moment
>> (search the OEIS with the string "FJS"). I have found this:
>>
>> (a)   1  1 3   1 1 3   1 3   1 1 3   1 1 3   1 3   1 1 1 3   3 ...
>> (b)  1 13 1 131 3 1 131 1 313 1 1 133 1 3 111 1 313 3 1 1 133 1 ...
>>      ----------------------------------------------------------
>> (c)  1113113131131131311133131111313311133111113313131111313331 ...
>
>>      ^
>> - the succession of digits in (a) and (b) are the same;
>> - when I "push" (a) into (b) I get (c);
>> - ... and (c) has the same succession of digits as (a) and (b)
>>       [except for the initial "1"].
>>
>> Does this ring a bell to someone ? Is it of interest ?
>
> You might want to check  A035263 "period-doubling sequence".
>


Hello Éric, and Joerg, and SeqFabs,


Nice finding. Your seq, Éric, inspires me this rather intuitive comment:

It shows a property which seems to me an original formulation  of one 
of the basic properties of some classical fractal sequences, which are 
self similar when dezooming (for instance: reading the even-index terms 
gives the seq itself), cf A025480:
0 0 1 0 2 1 3 0 4 2 5 1 6 3 7 0 8 4 9 2 10 5 11 1 12 6 13 3 14 7 15 0 
16 8

...They are builded so that any dezooming (which reveals the 
self-similarity) has to be regular or rigid.

In comparison, your seq (different than a period-doubling one, isn't 
it?) gives itself (so it is still a fractal one) when dezooming in a 
rather "slackness" mode (like the melting clocks of the painter 
Salvador Dali, which are still clocks)!
...a "slackness" mode although perfectly determined by your FJ rule!

See you

Alexandre