To download:
https://itunes.apple.com/us/app/nekoatsume/id923917775?l=ja&ls=1&mt=8
Neko atsume (ねこあつめ) is a virtual backyard for cats to show and play. You buy food and toys to feed and attract them, and they will give you cat money so that you can buy more toys. It is relaxing, and super super cute. Different cats will show up including mysterious cats and you can capture them in the album when they appear.
Their character, animation and sound design are all engaging and relaxing.
Screenshots:
A blogger review: http://kuroo10.blog.fc2.com/blog-entry-1.html
Their Official site: http://nekoatsume.com/games/neko/other/index.html