Everyone gets one square. The map grows by a square every time somebody new shows up, so it never runs out of room.
Bring a friend, get a square
When someone signs up and puts your name in, you get another square. Up to three extra, four in total.
You choose where each new square goes: tap any empty square on the map to drop it there.
Keep them apart and paint each one separately, or join them into one big picture: four in a row, two by two, however you like. Nothing moves unless you ask it to.
counting squares...