Algorithm putting point into square with maximal minimum distance

Mikulas, I found a page full of image examples of possibly optiimal, or currently best known solutions. It's not mine, so use it with your own risk.

See

http://www.ime.usp.br/~egbirgin/packing/packing_by_nlp/numerical.php?table=csq-mina&title=Packing%20of%20unitary-radius%20circles%20in%20a%20square

Source:

http://www.ime.usp.br/~egbirgin/packing/packing_by_nlp/

You could do an N body simulation where the points repel each other, perhaps with a 1/r^2 force. The movement of the points would obviously be constrained by the square. Start with all the points approximately in the centre of the square.

This is the circles in square packing problem.

It is discussed as problem D1 in Unsolved problems in geometry, by Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy, page 108.

Pages 109 and 110 contain a list of references.