So yeah, I would like to achieve something like this:
but with a noise texture inside the Blender Cycles materials.
Been searching for a while now, and only found this one that was dependent on camera angle, so it would change the noise position every time the camera moved.
Anybody have any words of wisdom on this? I keep getting some very pretty, but not very useful results 
Make yourself a utility node that does polar conversion (Blender doesn’t have atan2, use radial texture instead), if using object texture coordinates it should resemble something like that depending on how you setup the scalars when you feed those new coordinates to a noise texture. Basic idea would be to increase x (angular circumference) more as a factor of y (radius). Polar conversion should be fairly straight forward, and you don’t even need it if you can live with UV unwrapping it to a proper shape instead. However…
…The biggest obstacle has to me been figuring out a way to make noise repetitive and seamless over modulo 1 (in one direction). I did come up with kind of a hack in this post, utilizing two noise nodes (so unfortunately slower than I would like).
I’m terribly dense when it comes to math, but I’ll try reading through the wiki page and your thread and do my best to understand 
Been struggling with this for a couple of days now… I’m a little surprised I didn’t stumble onto the solution by mistake.
Will someone help me with the math? I’m a complete Jupiter when it comes to math. Very dense 
I could really use some help with this… Any help at all would be very appreciated
you could try something like this:
didn’t look very deep into all possible formulas for hyperbolic coordinate systems, but here’s one of them: s=2u/(1+u[SUP]2[/SUP])
(taken from here)
Thank you so much, I’ll try both and see if I can make it work 
Awesome that you took the time to figure this one out for me!
