Quadtrees are also quite useful for generating fractals. A very related project of mine, Lambda Screen [0], explores this by encoding these functional quadtrees directly in lambda calculus and rendering the structure based on Church booleans being true (white) or false (black).

With fixed point recursion, this allows for very tiny definitions of IFS fractals. For example, fractals like the Sierpinski triangle/carpet only require ~50 bit of binary lambda calculus [1] [2]!

[0]: https://text.marvinborner.de/2024-03-25-02.html

[1]: https://lambda-screen.marvinborner.de/?term=ERoc0CrYLYA%3D

[2]: https://lambda-screen.marvinborner.de/?term=QcCqqttsFtsI0OaA