Sphere Wrapped Perlin Texture

Hello there! I have a quick question. I know it isn’t possible to perfectly wrap a rectangular texture around a sphere without some kind of distortion. However, if I am randomly generating the appearance of the of a sphere by a perlin texture what would the best way of going about that be? Thanks for your help!

the correct method for this kind of texture wrapping is to use a 3D perlin function. rather than using the pixel cords to generate their color use the 3D point in local space that each pixel corresponds to after it has been wrapped onto the model. the result look amazing with just perlin but if you want an even smoother effect you could use a 3D simplex noise function.