Vi Hart's doodling videos and a 4 year old son interested in mazes has made me wonder:
What are some interesting mathematical "doodling" diversions/games that satisfy the following criteria:
1) They are "solitaire" games, i.e. require only one player; 2) They require only a pencil and blank sheet of paper; 3) They don't rely on abstract mathematical language/substitutions. More precisely, I'm interested in "picture" type games with very simple rules, and not the cheeky answer: "mathematics".
What I'd really like to see is a game with simple rules that, out of the planarity of a sheet of paper, somehow "generates" a maze for the player from the "automaton" type rules...A good starting point may be a solitaire version of dots-and-boxes or something like this...
If such a thing is impossible, under certain simple desirable assumptions, I'd like to see proofs of such a fact, too.
You could draw an elementary cellular automaton with random initial row.