In FRACTRAN, every program is a list of functions

Incorrect title - every program is a list of fractions - makes a big difference.

I remember Conway explaining this to me in 1984. It seemed so obvious when he talked about it, and then when I later tried to reconstruct it, completely impossible.

He recently described his latest explorations to me and I distinctly remember during that thinking: Is this insane? Or is it genius? How can I tell? It's certainly bizarre.