Is there any way to gain access to the algorithm that wolfram alpha uses? More specifically, I want to pack small circles in hex and square patters in a larger cicle (https://www.wolframalpha.com/examples/GeometricPackingIn2D.html), but wolfram alpha only does this up to a number of 1,000.

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    $\begingroup$ Realted demonstration project: Circles Packed in a Circle. Disclaimer: there is no algorithm there, only plain list of circle positions up to 100 circles. See also (99580) for hexagonal packing approximation. $\endgroup$ – ybeltukov Dec 1 '15 at 13:20
  • $\begingroup$ Yeah, the code for that one is oddly unsatisfying. I don't know if someone here has access to the methods used by alpha, I suspect it's off-topic for this site. You would have better luck rephrasing the question along the lines of "How can I use Mathematica to find the densest packing of _ circles in _ shape?" Even better if you can give it a shot yourself and ask for improvements to the code. Some of these might be relevant. $\endgroup$ – Jason B. Dec 1 '15 at 13:25
  • $\begingroup$ The thing is, I'm not interested in the densest packing of circles. I'm interested in the required radius to pack N circles in square and hex patterns. $\endgroup$ – J Doe Dec 1 '15 at 18:00