Comment by kamens

15 days 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

6 comments

kamens

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ogogmad  15 days ago

Have you considered finding a conformal transformation† that maps a square to any other possible shape, as long as the shape doesn't have any holes? Such a transformation always exists by the Riemann Mapping Theorem, and is unique as long as you specify in addition (1.) which point the square's centre maps to, and (2.) the angle of rotation around that point. Not sure if anyone's ever tried that.

If you actually want more aesthetic freedom, you can compose with an arbitrary diffeomorphism of the square to itself. But I think that might usually look worse.

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

  • ogogmad  15 days ago

    P.S. This suggestion would eliminate your pinch points.

    • kamens  14 days ago

      i'm torn between my stupidity re:your first comment and my love of eliminating pinch points (now you're speaking my language). i need to read up a lot to better understand your suggestion!

      (most pinch points are gone these days, it just required a lot of edge case hunting)

kamens  15 days ago

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.