A dynamic Houjin (square) and a symmetric Houjin

Abstract

A Houjin is an n by n square lattice with each cell containing a symbol (such as a number or a letter). Further, these numbers or letters are designed to exhibit symmetry. For example, a magic square is a Houjin where the embedded symmetry is that the numbers in each row, column, and a center diagonal have an equal sum. This article reports a new Houjin: a dynamic Houjin. A dynamic Houjin changes its numbers at each time step while satisfying the symmetry as a Houjin (a magic square). The dynamic Houjin has a further symmetry in a time dimension, i.e., the sums of the numbers in each cell are identical.