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Packing and tiling: - circles and spheres      Download demo version!


1 - packing equal circles in a square
2 - packing equal circles in a circle
3 - packing equal spheres in a cube
4 - packing equal spheres in a sphere


As you probably know, the problems of packing are all NP and are of a great theoretical and practical interest.

The natural question is, how the Critticall would handle them. Since there is a huge academic and hobbyist tradition for solving this kind of riddles, it was not hard to find some challenges and to do some comparisons how good we really are with this method. It turns out that the Critticall's engine is just fine! What was accomplished by many different people with many different algorithms/programs and (super)computers throughout the decades, is quite easily matched and/or surpassed by the program you may download and try.

The 256 circles inside a square, an example from www.packomania.com has been solved (from scratch) in a matter of hours. Now as the task is mechanized, get your own machine at www.algit.eu and contribute to the packing saga, which has just begun. Be an explorer at the packing frontier, have fun and do science yourself!


The record dense packing of 256 equal circles inside a square, obtained by the Packntail software:



The record dense packing of 72 equal spheres inside a cube, obtained by the Packntail software:




The record dense packing of 72 equal spheres inside a sphere, obtained by the Packntail software:




28-March-2010
The record dense packing of 257 equal circles inside a square, obtained by the Packntail software:




12-April-2010
The record dense packing of 258 equal circles inside a square, obtained by the Packntail software:




12-April-2010
The record dense packing of 53 equal spheres inside a sphere, obtained by the Packntail software:



26-April-2010
The record dense packing of 66 equal spheres inside a cube, obtained by the Packntail software:




30-April-2010
The record dense packing of 251 equal circles inside a square, obtained by the Packntail software: