Read up on Conway's Game of Life. Modify one of the sample codes which implement a simple board game/demonstration. First, open and run the board games.
Source code for the samples are here: src
1. You could move a different piece around the board, say a rook or a bishop.
2. Examine Conway's Game of Life (search online, many entries), and look at gliders. You could implement a different glider on the life.py code.
3. You can, of course, resize boards, change speeds, and such.