For test purposes I need parametric Jordan curves that are complicated in the sense of having many inflection points and ideally no symmetries. When doing online search I always land at complex analysis and curves related to conformal maps.

Explicit formulas or recipes for generating such curves would be great; even better if sample images could be provided.

I need those kind of test curves for checking an algorithm for generating characteristic functions from closed curves and for checking the approximability of those functions.