Very cool! This basically encodes a quad-tree of bits where every except one quadrant of each subquadrant recurses on the parent quad-tree.

The corresponding equivalent of functional programming would be Church bits in a functional quad-tree encoding \s.(s TL TR BL BR). Then, the Sierpinski triangle can be written as (Y \fs.(s f f f #f)), where #f is the Church bit \tf.f!

Rendering proof: https://lambda-screen.marvinborner.de/?term=ERoc0CrbYIA%3D