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

Maybe you can find a geometrical property that is true only for 200-packings and not for 199-or-less-packings. Then build the packing incrementally while conserving the property.

For example, you may examine several available 200-packings and measure the maximal distance between all circle centers -- m. Then construct a packing incrementally, preserving m.

I don't know how often such a construction succeeds, but you can add more invariant properties as you wish to increase the chance of success.