So, if you really want your mind blown,  check out the interrelationship between
binary, Gray code, and N-dimensional Hilbert curves.

https://corte.si/posts/code/hilbert/portrait/

https://github.com/cortesi/scurve

https://www.grant-trebbin.com/2017/03/calculating-hilbert-curve-coordinates.html

https://en.wikipedia.org/wiki/Gray_code

The following makes me suspect that it might be possible to make a procedural
function-based pattern that can infinitely tile the plane and not require an
iterative-type solution.  Then one could pick any region of the plane for the
camera to look, and you'd have a proper Hilbert curve that was simple (and fast)
to calculate.

https://rantonse.org/art/hilbert-tiles

Very much like the Direct Stochastic Tiling:
https://news.povray.org/povray.advanced-users/thread/%3Cweb.650ba428c90fe1dd1f9dae3025979125%40news.povray.org%3E/

(Somewhat related / of interest:)
https://spacefillingcurves.wordpress.com/category/tiling/

- BE

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