I remember once playing a game where you had to look after an island of people that had crash landed and they would work and build and grow in real time (i.e. you would have to say "collect wood for fire" then come back in a couple of hours and there would be a pile of wood). They would also make more little island people who would grow up over time.
I was wondering if that style of game had a specific genre or category so I could look it up and read more about it.