Finding this article was a real relief. I was starting to think I was the only person interested in making up projections.

How would I go a stage further and define my own projection for the map? By that I mean not a tweak to Winkle Tripel, Gnomonic nor Peirce Quincuncial, but an equation that I type in to define the form that the map takes?
Code:
+proj=custom1
I would probably start by defining custom1 as an existing projection like Mercator and apply it to an image of Earth to make sure things are working right, then try something from scratch.

Thank you