Comment by kamens

14 hours ago

I used Jamis' book extensively to build this AI tool for generating custom mazes of any shape! https://kamens.com/blog/generating-custom-mazes-with-ai

Have you considered finding the conformal transformation† that maps a square maze into any other possible shape, as long as doesn't have any holes? Such a transformation always exists by the Riemann Mapping Theorem, and is furthermore unique as long as you specify a base point and a direction. Not sure if anyone's ever tried that.

† - That is, preserving all angles, including right angles. The terminology stems from the output angles conforming (???) with the input angles.

The main difference between the above tool and most custom shaped maze generators out there is breaking the assumption that the maze's outer shape must be defined by adding or removing regularly-shaped cells along the edge.

To have mazes look more human drawn, cells need to be irregular and the inner walls need naturally follow the contours of the outer shape.