This is a bit of a two-fer. Martin is right that Piers Anthony's OX features Conway's Game of Life.
She looked at him suspiciously. "You mean this has been done before?"
"This is a once-popular game invented by a mathematician, John Conway, back in 1970. He called it
'Life.' I have often whiled away dull hours working out atypical configurations."
Found it with your help, Valorum, thank you!
It was Strange Attractors by William Sleator.
Apparently the device was a modified calculator, and it was used for time travel (which leads to a split timeline and antagonist versions of two of the main characters).
Could this be "The Lotus Eaters" by Stanley G. Weinbaum?
A month after the events in "Parasite Planet", Hamilton "Ham" Hammond and Patricia Burlingame are married, and thanks to Burlingame's connections, the two have been commissioned by the Royal Society and the Smithsonian Institution to explore the night side of Venus. There they find a species of warm-...
This sounds very much as though it could be The Zero Stone by Andre Norton (which also has a sequel - "Uncharted Stars"), first published in 1968.
The young man's name is Murdoc Jern and he has an alien companion, kind of like a cat, called Eet.
One of the most familiar covers (at least to me) is:
There's a reasonably complete write-up by Judith Tarr on the ...