I would like to plot Scherk's first surface which is defined on a checkerboard of the plane, e.g. $-\frac{\pi}{2} < x < \frac{\pi}{2}, -\frac{\pi}{2} < y < \frac{\pi}{2}$ and $\frac{\pi}{2} < x < \frac{3\pi}{2}, \frac{\pi}{2} < y < \frac{3\pi}{2}$.
The patch is $\mathbf{X}(u,v) = (u,v,f(u,v))$ where $f = \ln\left( \frac{\cos(x)}{\cos(y)}\right)$.
ContourPlot3D[Exp[z] Cos[y] == Cos[x], {x, -π/2, 3 π/2}, {y, -π/2, 3 π/2}, {z, -π/2, 3 π/2}]
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