After encountering the enticing pattern produced by continued fraction functions (also shown above) I fell down an extended rabbit hole of pattern chasing that somehow managed to lead me from generalized Golden ratios and their power sequences to "extended Fibonacci sequences" and various widely applicable number sequences embedded in them that are somehow meaningful also in the study of quantum mechanical spin systems? The rabbit hole and its story is so long and odd that I had to add a theory section so I have a proper place to write it all down.

Sometime later while reading a fractal related discussion I bumped into an X-ray diffraction pattern that was instantly familiar to me. Do you see it too?