World space to spiral space?

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

Something like this?

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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.

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.