This app was mentioned in 4 comments, with an average of 1.00 upvote
There are imitations of that game, I'm not sure of their names however. I heard that game's creator is working on a new app-game or something for either Apple or Amazon?
For Android though: "I Love Hue" is supposed to be super soothing. I'm not big on text game's, but I am just starting to enjoy 'Seedship," since it is simple, compelling, and thoughtful. Angry Birds 2 is fun, but I found the Star Wars versions to throw too much at me.
"Aquavias" is the most soothing and comforting game I've played. It won't have the sense of repetition you're seeking, but building the beautiful waterways is easy and the music is really special.
The original Sonic the Hedgehog is on Android these days and can really put you in a trance!
There's one game I really think you'd like. You'd have to be patient though, as all hand-eye coordination games should be played in small chunks over a few days to start. Each time the brain sleeps it grows a ton of new physical connections that allow for deft new movements... Update: I barely found it! Took me more than a half hour. The game is called Polyforge. It's simply amazing. The official Android link: POLYFORGE