How does one map an existing locally-similar pseudorandom pattern like the galaxy image onto a torus, Klein Bottle, or other closed shape? I know that with a ge

How does one map an existing locally-similar pseudorandom pattern like the galaxy image onto a torus, Klein Bottle, or other closed shape? I know that with a generated pattern (e.g. Perlin noise) you automatically get that by taking the value of the noise function at the surface coordinates, but I have no clue about using existing planar images.