3dxml at the bottom.

This is study on hyperbolic tilings

here below is an explanation on how to build such tiling and a summary on inversions

In short, and I understand it, hyperbolic space is where most of the time, lines are circles (segments are arcs).

in French, but academic documentation can be found searching for "hyperbolic tilings or pavings"

I works in the complex plane because then I can use inversion as particular case of a mobius transform (az+b)/(cz+d) -> inversion is 1/z

For complex transformation and operations, I have user operators (zbar, z1 X z2, etc, mobius transform etc). that you can check in the model

the base logic

1. create the base tile (central one). shame I did it 1 year ago and cannot crack the formula again (despite doc and chatgpt...)

2 loop

         2.1 make the inversion of the tile by all its sides

         2.2 remove from the loop the tiles that are overlapping

         2.3 stop the loop when the tile size is too small

here are some pictures