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With the solution above suggested by David G. Stork, I made this complete (?) working solution. I'm now wondering if it could be improved in some way. Currently, it's a bit slow. SeedRandom[]; f := {RandomReal[{0, 10}, 2], RandomReal[{0.5, 3}]} l = {f}; While[Length@l < 10, While[k = f; Not[And @@ ((# + k)[[2]] < EuclideanDistance[#[[1]], ...


The trick is to place some random non-overlapping Disks in your square area, then use the DistanceTransform to find a point in your square area that is the farthest from its nearest disk. (Such a point will be equidistant from at least two disks--generally three or more disks.) Place a new disk centered at this point, with its radius equal to the distance ...

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