Hi Dear community,

I want to randomly distribute spots on a sphere (never mind the degree of randomness for now):

I did the following:

Random choice of coordinates:

Psifix = Random[Real, {0, 2 Pi}]
Phifix = Random[Real, {0, Pi}]

My coordinates:

a[u_, Psi_] = Cos[Psi] Sqrt[1 - Cos[Phi]^2];
b[u_, Psi_] = Sin[Psi] Sqrt[1 - Cos[Phi]^2];
c[u_] = Cos[Phi];

The plotting:

ParametricPlot3D[{Cos[Psi] Sqrt[1 - Cos[Phi]^2], 
  Sin[Psi] Sqrt[1 - Cos[Phi]^2], Cos[Phi]}, {Psi, Psifix - 0.05, 
  Psifix + 0.05}, {Phi, Phifix - 0.05, Phifix + 0.05}]

This spans a surface around the randomly chosen point as a function of theta and phi.

The problem is as follows: I would like to not have one random number but be able to plot let's say 10 of these surfaces meaning that I want an array of Phifix's and Psifix's and find the surface for each of them and plot all of them in one plot .

How would you advice me to do that? I am sorry if it is trivial but I am new to mathematica.

Thanks,

Marcel.