residual errors are within the prescribed tolerance parameter $\varepsilon \sim 10^{-15}$ and never exceed $10\varepsilon$.

![*A bi-periodic wave pattern $B(x,y)$, $\Omega = [-30, 30]\times[-15, 15]$ and $\omega = 0.18$. $B$ can be described by the $1\times 4$ discrete pattern $E = {}^t(r, b, r, b)$ on the two-letter alphabet $\{r, b\}$ (red spots code negative values far from zero and blue spots refer to positive values far from zero).*[]{data-label="fig:f1"}](figs/gstates/60x30_0_18_select.eps){width="75.00000%"}

![*A bi-periodic wave pattern $B(x,y)$, $\Omega = [-30, 30]^2$ and $\omega = 0.18$. The box delimits the elementary $6\times 10$ discrete pattern of blue ($b$), red ($r$) and white ($w$, denoting the values around zero) spots identified to describe $B$ by substitutions on the three-letter alphabet $\{r, b, w\}$. For symbolic coding see caption of Figure \[fig:f0\].*[]{data-label="fig:f2"}](figs/gstates/60x60_0_18_select.eps){width="75.00000%"}

[figs/gstates/60x40\_0\_18\_select.eps]{} (24,54.5) [$\sigma(b)$]{} (43,54.5) [$\sigma(a)$]{} (24,47.5) [$\sigma(c)$]{} (43,47.5) [$\sigma(d)$]{} (24,39.5) [$\sigma(\bar{b})$]{} (43,39.5) [$\sigma(\bar{a})$]{} (24,30) [$\sigma(\bar{a})$]{} (43,30) [$\sigma(\bar{b})$]{} (24,22) [$\sigma(d)$]{} (43,22) [$\sigma(c)$]{} (24,14) [$\sigma(a)$]{} (43,14) [$\sigma(b)$]{}

![*A bi-periodic wave pattern $B(x,y)$, $\Omega = [-30, 30]\times[-60, 60]$ and $\omega = 0.18$. The box delimits the elementary $32\times 66$ discrete pattern of blue ($b$) red ($r$) and white ($w$) spots identified to describe $B$ by substitutions on the three-letter alphabet $\{r, b, w\}$. For symbolic coding see 