Generate random inside a loop in postgresql

I want to execute several times (lets say 30) an "experiment" that involves random numbers

My approach was:

select  
  rnd  
from 
  generate_series(0,30) as l,   -- number of times
lateral (
  select random() as rnd -- the "experiment"
) as t ;

You can read this as "Execute 30 times the experiment".

The problem is that that code generates 30 exact numbers.

Please NOTE: The "experiment" part obviously is more complex, but somewhere in it, it creates hundreds the random numbers per experiment run. i.e. I want to generate those hundreds of random numbers, 30 times. This is important, because I know that I could execute

select random() from generate_series(0,30)

and get 30 different random numbers, but that is not what I intend to do.