Mathematica : Perlin like distribution on a sphere

[Barnak]

I need to generate a set of random points on an unit sphere, using Mathematica. I can do it for a simple homogeneous (i.e. uniform) distribution of points using the following coordinates :

RandomPoints[u_, phi_] := {Sqrt[1 - u^2] Cos[phi], Sqrt[1 - u^2] Sin[phi], u},

with uniform random variables u in [-1, 1] and phi in [0, 2 Pi].

However, I would like to define a distribution that feels more "natural", i.e. Perlin-like (take note that I don't know how to define "Perlin noise", mathematically).

What do you suggest ?

 

[Adrmay]

One way to generate points on the unit sphere with a Perlin-like distribution is to use the spherical coordinates system. That is, we can define our uniform random variables u in [0, 1] and phi in [0, 2 Pi] and then convert them into spherical coordinates using the following equations:theta = acos(2u - 1)phi = 2Pi * phiRandomPoints[u_, phi_] := {Sin[theta] Cos[phi], Sin[theta] Sin[phi], Cos[theta]},This should give a more Perlin-like distribution of points on the unit sphere.