I assume there's fanfic shipping of automata...

(If you don't recognize that use of "shipping", don't google it at work.)

https://tvtropes.org/pmwiki/pmwiki.php/Main/Shipping should be reasonably safe for work. As long as you can avoid getting sucked in to an all-day wiki bender.

short for relationship

conwaylife.com isn't just for GOL, although it is the main subject, there is an Other Cellular Automata forum. also it's not really a fansite, it's a bit more academic than what would be considered a "fansite".