These great pages of generated images and their mathematics (simple to formal math), on a Mathematica site.
(I can’t find my copy of d’Arcy Thompson’s classic On Growth and Form.)
Youtube and Google came up empty.
I’ve seen a time-lapsed film of spiraling vines; I think such a project with sea shells would be mind blowing.
My apologies. The cite/site above is hosted by the Mathematical Sciences Digital Library.
Growing shells contain living animals which move around too much to make time lapse photography feasible. (Even clams and mussels will be opening and closing their shells periodically.) Besides, shell growth is much slower than the growth of vines or the opening of flowers that may take place over a period of just a few days.