Antigrid

Work in progress

Take normal space and divide in square tiles. You go through the top of a square, you end up in the bottom of another. Go Up, Left, Down, Right and you're back at the start. Now, take the grid, cut it, and paste it as you please. Up is Left, Down depends on where you came from, and straight lines cross themselves.

Welcome to Antigrid.

Arrow keys to move around, left mouse to alter the grid, right mouse to change tile value, center click to teleport player.