What you see here is the graph of the 6j symbol with all arguments being $n=1000$, except one as free variable $x$. This cries for numerous questions:
- Why the "split" $x \mod 3$? (I highlighted one branch in the second pic.)
- Why the sinusoid curve?
- Why the "crash" at $x\approx 7/4*n$? (It is identically zero only at $x>2n$.)
There exists an asymptotic formula for 6j symbols but I doubt it explains these observations (which are by the way independent of the exact arguments - if I set one to $999$ instead of $1000$, nothing changes). Given the importance of 6j symbols in physics, I would be very surprised if I am the first person to make this graph, especially as MATHEMATICA for small $n$ quickly gives an exact polynomial to play with.
