How to generate a star onto a render texture with spherical warping

How would one proceduraly generate a star in a compute shader that looks like one of thes two at any size needed. Also any way transfer this into a spherical map, would be appreciated. Goal is to create a spherical skybox of stars, (stars a pre generated, and not just decoration).

So far got accurate positioning of the stars on the spherical skybox but lack the equations to get it looking like I want.

Preferably the one on the right.

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This below is what I currently have, ~~5 to 15ms processing time, little over 30k stars

enter image description here

Using Unity2019.3.1f1, needs to be compute shader compatible. (if not I will convert it somehow) Render Texture output.