TITLE: The fractional part of $n\log(n)$
QUESTION [12 upvotes]: When I was thinking about my other question on the sequence 
$$p(n)=\min_a\left\{a+b,\ \left\lfloor\frac {2^a}{3^b}\right\rfloor=n\right\}$$
I found an interesting link with the sequence
$$q(n)=\{n\log(n)\}=n\log(n)-[n\log(n)]$$
the fractional part of $n\log(n)$.
If we draw the sequence $q$, we get this (for $n$ up to $520$, $5\,000$ and $30\,000$ respectively):



We can see some gaps looking like parabolas.

What is causing those gaps? Why do they look like this?

In my other question, we can observe similar structures:

An answer is telling me that it is due to the continued fraction of $\log2/\log 3$.

Could the two questions be linked?


Edit.
Thanks to Gottfried Helms idea, here is some more drawings with the moduli varying.
The moduli will take those values respectively:
$$1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100.$$
A modulus of $1$ corresponding to the fractional part.

REPLY [3 votes]: Not an answer but some more illustration (by my own couriosity)
I*ve looked at your function mod 10 and 100. Nice pictures... 

 
Ok, just for fun: "fine wood". Also see, how the picture can nicely be stacked vertically; here I stacked the mod-100 picture 3 times: