Getting an elephants trunk to wiggle II

Enrico Fermi told Freeman Dyson "with four parameters I can fit an elephant, and with five I can make him wiggle his trunk".

Phil Nelson kindly brought to my attention a nice paper
Drawing an elephant with four complex parameters
by Jürgen Mayer, Khaled Khairy, and Jonathon Howard

There is also an interactive Mathematica Demonstration that allows you to see how the quality of the fit increases with the number of parameters [but does not have a wiggling trunk!].