  We show that any dynamics on any planar set $S$ discrete in some domain $D$
can be realized by the postcritical dynamics of a function holomorphic in $D$,
up to a small perturbation. A key step in the proof, and a result of
independent interest, is that any planar domain $D$ can be equilaterally
triangulated with triangles whose diameters $\rightarrow0$ (at any prescribed
rate) near $\partial D$.
