Interpreting Figure 1 in the "On Lattices, Learning with Errors, Random Linear Codes, and Cryptography"
The points of $\mathbb Z/q\mathbb Z$ are mapped to $\mathbb R/\mathbb Z$ and plotted in a circle.  The plot shows
\begin{align*}
  x &amp;= \sin (2\pi i/q), \\
  y &amp;= \cos (2\pi i/q), \\
  p &amp;= \Psi_\alpha(i/q).
\end{align*}
for each $i$ in the least nonnegative residues modulo $q$.

The following gnuplot script gives a similar graph, for $q = 31$:


set parametric
set samples 31
psi(alpha, r) = exp(-pi*(r/alpha)**2) + exp(-pi*((r - 1)/alpha)**2)
splot [i=0:30] sin(2*pi*i/31), cos(2*pi*i/31), psi(0.1, i/31) with points