[seqfan] Re: This is a Penrose tiling?
Brad Klee
bradklee at gmail.com
Tue Jan 7 22:32:19 CET 2020
J-PA: To me this is not "the" Penrose tiling but "a" Penrose tiling.
(of course depending of what the definition of a Penrose tiling is
or should be)
One definition would be: A tiling is *a* Penrose tiling if and only
if it is "Mutually Locally Derivable" to *the* Penrose tiling.
This was not proven but implicitly assumed(?) in the Shutov article,
so I think it's fair to start with a skeptical attitude. If it is a Penrose
tiling by MLD, what is the transformation to the canonical form?
NJAS: Maybe you could generate 1000 terms and send them to me,
if you don't know how to extend the sequence in the OEIS entry?
Using optimized code, I can generate 100 terms in under 15 minutes,
see follow-up post at:
https://community.wolfram.com/groups/-/m/t/1854730
Using the same code, 1000 terms should be doable in a day using
one processor at 2.7Ghz, but I think it's a distraction. If the tiling is
MLD then we should find how to obtain it from the Penrose tiling
before doing anything else.
Even then, it seems the R. Sigrist's sequences are a better place
to start. We know that there are finitely many vertex types, so the
sun and star sequences can each be projected to component
sequences, one for each vertex type.
Will the component sequences tell us anything interesting about
the four separate trends on the scatter plots? I don't know.
See also:
https://oeis.org/A302841/graph
https://oeis.org/A302842/graph
--Brad
More information about the SeqFan
mailing list