ねこあつめ (Neko Atsume) is a cat collecting game for Android and IOS , which I became kind of obsessed with playing. In the game, you buy food, toys, and furniture for your yard in order to attract different types of cats. You can simply watch the cats, take pictures of them, and receive gifts from the them once they leave. Once the cats leave, they often leave you a reward of silver/gold sardines (which you use to buy the cats food, toys, and furniture). The more they visit you and become friendly with you, they will leave a memento for you to keep.
In the game, there are 53 cats total. 19 in which are considered rare. Different toys and food attract different/rare cats. If you want more cats to come and visit, you can also expand your yard. There are six different styles for the extension: original, modern, western, sugary, zen, and rustic.