My favorite casual computer games are puzzles that allow me to pore over the solutions for hours. I want lots of little things to go whirr! and click! and then do my bidding. If you have not played Trainyard yet, I strongly recommend checking it out! (You can start with the free edition, Trainyard Express, which thankfully does not have any advertising or in app purchases, by the way.) Trainyard lets you draw tracks with your finger, and little locomotives are traversing them in funky patterns, changing their colors on the way, before either crashing or finding their destinations.
Trainyard is in principle Turing complete (i.e. you could build a computer in it), but Trainyard's playing area is limited to 7x7 fields, and you cannot place any of the interesting stuff yourself (like replicators and color changers), so practically, that's not possible.On the other end of the spectrum, there is Minecraft, the famous open-ended, almost infinitely large brick-laying playground. Among other things, Minecraft is a three-dimensional cellular automaton, with a playing field that is 30 million cells wide and deep, and 255 cells high. Cells may interact with each other up to a distance of 15, with most of the interaction limited to the directly adjacent cells. Using specific materials that act as conductors, isolators, switches and repeaters, players can wire up their virtual fortresses with button-operated trap-doors and lighting. And some relentless players have figured out how to build computers in the game.
