User:Richard777/Sandbox

Periodic Matrix Set

A "periodic matrix set" is a set of square matrices. Each matrix within a set must be a different size. There is no limit to the number of matrices in a set, however a set may be specified to contain a fixed number of matrices.

Each matrix must contain a "root cell". A root cell must be located at one corner of each matrix. All root cells must be located at the same corner of each matrix within a set.

Each cell within each matrix within a set contains a number which is associated with some type of periodic distribution. The periodicity is defined by "partial square rings" (rings) or "layers" of cells adjoining a root cell on two sides. All cells within the same ring, (even if they are located in a different matrix) have a similar "period". If a matrix contains (n+1)2 cells then the outermost layer contains 2n+1 cells which are all included in the same period.

Combined sets are possible. Four sets may combine so that all root cells are adjacent. This gives an even number of cells on each side of a resultant matrix with all root cells located in the center.

Periodic matrix sets have application to chemistry and particle physics. xxxxxxxxxxxxxxxxxxxxxxxxxxxxx