[seqfan] Re: Glass worms
Mitch Harris
maharri at gmail.com
Mon Mar 9 19:48:23 CET 2009
> Take a finite row of glasses, each one containing an
> interger number of liquid-units (zero = empty glass)
>
> Procedure:
>
> - take the leftmost glass,
> - consider the number k of liquid-units it contains,
> - empty the glass in the k-th glass on it's right,
> - put the now empty glass at the right end of the row;
> - start the procedure again.
Your procedure is vey reminiscent of (but not identical to) siteswap
notation for juggling patterns:
http://www.research.att.com/~njas/sequences/?q=siteswap&sort=0&fmt=0&languag
e=english&go=Search&n=100
explanation at
http://www.juggling.org/bin/mfs/JIS/help/siteswap/
But rather than thinking of you glassworm sequences about numbers in decimal
(a much too contingent selection), think about number of unique patterns
(with restrictions like max amount in a glass).
...
> Should we represent a glass-configuration as a string of
> characters, the above sequence would look like:
> (a) 12410 --> (b) 03410 --> (c) 34100 --> (d) 04130 -->
> (e) 41300 --> (f) 01304 --> (g) 13040 --> (h) 04040 -->
> (i) 40400 --> (j) 00404 --> (k) 04040 --> (h) (loop)
>
> What would be the seq. W(1) of integers (like 12410 or 13040)
> which end in a loop?
Isn't it obvious that they all end in a cycle? Or do you expect to encode a
TM-like thing?
(they all have to loop eventually, because you have a finite amount of
liquid so the # of glasses is finite).
Mitch
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