What's the genre of game where you have to look after a community that grows in real time?

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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.
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What is genre in games?
A video game genre is a specific category of games related by similar gameplay characteristics. Video game genres are not usually defined by the setting or story of the game or its medium of play, but by the way the player interacts with the game.How many types of game are there?
Games are a structured form of play. These can include goals, rules, art, environments, stories, challenges, characters, items, powers, rewards, exploration and interaction between players. The following are common types of game....Win-Win.Overview: GamesTypePop CultureDefinitionStructured forms of play.1 more row•Feb 3, 2019What is the importance of community games?
The communities formed around playing, watching and talking about video games can become valuable subcultures, not only to the people who find friendships and support there but also to game developers and other companies.what. (Bo Burnham FULL SHOW HD)
Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.
Images: Matheus Bertelli, Allan Mas, Allan Mas, Monstera