Nehaveigur

The board game Go is famous for having extremely simple rules yet having an almost unlimited number of ways to play it.

The mathematician John Horton Conway was good at coming up with simple games that resemble Go in that they have simple rules and complex outcomes. This includes games that can be played with pen and paper, but also a cellular automaton he called the Game of Life. This website is great for playing around with the Game of Life and getting an intuitive feel for it. For going deeper, I recommend A New Kind of Science by Stephen Wolfram.