Coherent Spherical Noise?

Question

Does anyone know how I might be able to generate the following kind of noise?

• Three inputs, three outputs
• The outputs must always result in a vector of the same magnitude
• If it receives the same input as some other time, it must return the same output
• It must be continuous (best if it appears smooth, like perlin noise)
• It must appear to be fairly random

EDIT: It would also be nice if it were isotropic, but that's not entirely necessary.

Answer 1

I've found a way, and it might not be very fast, but it does the job (this is c-like pseudocode designed to make porting to other languages easy).

vec3 sphereNoise(vec3 input, float radius)
{
    vec3 result;
    result.x = simplex(input.x, input.y); //could use perlin instead of simplex
    result.y = simplex(input.y, input.z); //but I prefer simplex for its speed
    result.z = simplex(input.z, input.x); //and its lack of directional artifacts

    //uncomment the following line to make it a spherical-shell noise
    //result.normalize();
    result *= radius;
    return result;
}