plotting the remainder r(n,x) as a function of n

29 Views Asked by At

I was graphing the remainder of the Euclidean division between an integer $n$ and an irrational $x$: $r(n,x) =n-x \cdot \lfloor n/x \rfloor$ when I stumbled on quasi-linear graph I cannot explain. Any idea how to calculate the slopes of the lines and why there is no lines for $x = \phi$, the golden ratio?

r(n,Phi):

r(n,Pi)

r(n,e)