Ideas for an algorithm for random distribution of circles in a square

Question

I am searching for a concept to distribute circles in a square randomly, so that they dont overlap. All circles are of the same size. The area covered by the circles can be high

Answer 1

If you'll sometimes have a high number of circles such that you are close to, or at, maximal packing, the best solution is to start with your circles maximally packed in some corner (which I guess is hexagonal packing) and then do a physical simulation where you add some "temperature", i.e. you randomly kick some circles and let them collide for some finite time.

I am afraid that with the other methods you might never be able to fit all your circles if you have so many circles that any valid solution would be close to maximal packing.