> "With four parameters I can fit an elephant, and with five I can make him wiggle his trunk."

Indeed: here are two papers on this topic:

Jürgen Mayer; Khaled Khairy; Jonathon Howard. Drawing an elephant with four complex parameters. 2010. https://pubs.aip.org/aapt/ajp/article-abstract/78/6/648/1042... Article without paywall : https://publications.mpi-cbg.de/Mayer_2010_4314.pdf

Dian Jin; Junze Yuan. Fitting an Elephant with Four non-Zero Parameters. 2024. https://arxiv.org/abs/2407.07909v1

Given that information can be encoded in a string of digits of infinite length, there is no limit to how precisely the elephant can be drawn. Any image file is a string of bits, a single parameter.