World space to spiral space?

Does anyone know how to encode two numbers as one value of a spiral?

Something like this? https://www.shadertoy.com/view/MtBcWz

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Yes! Very much like that.
It’s going to take some more consideration, but that’s a huge help.
My goal was to create a spiral of fixed size, find the nearest point on the spiral. Find its distance along the spiral, and use that single number to encode a position. Sadly, I am feeling stronger at concept than execution right now. Another method I’m trying is encoding by length along a linear function that’s been fract into a square.

for anyone paying attention…that’s an archimedean spiral.
https://rosettacode.org/wiki/Archimedean_spiral

It has the unique mathmatical property that as you draw from the center outward, each ring is equidistant. This makes it useful for texture projections or encoding of information.