  We show that any dynamics on any discrete planar sequence $S$ can be realized
by the postsingular dynamics of some transcendental meromorphic function,
provided we allow for small perturbations of $S$. This work was influenced by
an analogous result of DeMarco, Koch and McMullen for finite $S$ in the
rational setting. The proof contains a method for constructing meromorphic
functions with good control over both the postsingular set of $f$ and the
geometry of $f$, using the Folding Theorem of Bishop and a classical fixpoint
theorem of Tychonoff.
