  The Weierstrass representation for minimal surfaces in $\mathbb{R}^3$
provides a flexible method for constructing minimal surfaces of arbitrary
genus. The topological limitations of minimal surfaces interfere with this
providing a more general geometric modeling tool. Minimal surfaces lie in the
larger class of harmonic surfaces, which in general don't have the same
topological limitations of minimal surfaces and can have complicated embedded
ends. In this paper we demonstrate the flexibility of using the Weierstrass
representation for harmonic surfaces to combine embedded harmonic ends together
to construct embedded harmonic surfaces of arbitrary genus.
