Patterns and structures in disk packings (Q1382391)

The authors investigate structures of packings of \(n\) circular discs in regions of various shapes. The packings are generated by a computational procedure. First random packings are obtained by a billiards simulation algorithm in a square with periodic boundary where the values of \(n\) are in thousands. The initial disc configuration in packings of second type is not random. The experiment begins with a known or conjectured optimal disc configuration. A so-called ``frustration'' is introduced by varying of boundary shape or disc size. These two types of packings have applications in material science and physics. In the third case the billiards algorithm is applied for small number of discs (from several tens to few hundreds) in circles, squares and equilateral triangles to construct dense packings.