Help ~

 Generate a clustered pattern in [0; 1]2 as follows:
(a) Generate n, say 20, independent cluster centers (which can be called
parents) that are distributed i.i.d. uniformly in the unit square;
(b) then m,say 100, daughters are assigned i.i.d. uniformly to these
parents and such that each
daughter is located i.i.d. uniformly in a disk of radius r = 0:1 centred
at her parent, under the periodic boundary conditions, i.e. the square is
converted into a torus.

I tried some but can not figure out the whole thing. 
Thank you very much for your time. 
Yours 
Wolfgang Amadeus