The classic dragon curve is an early example of a plane-filling fractal curve with a complex shape. As an exercise in comparing the morphologies of similar curves, a taxonomy is being formulated to enable classification and discovery of new curves. With an eye toward biological metaphor and self-similar aesthetics, a collection of designs is being developed in parallel with the formulation of this taxonomy. It is based on two kinds of complex number integers (forming a square or triangular lattice in the plane) which provide an algebraic framework for categorizing and generating curves. Some techniques for rendering these curves are described, intended to bring out the inherent characteristics of families of curves.