Equivalently, in a torus divided into regions, it is always possible to color the regions using no more than seven colors so that no neighboring regions are the same color. (Contrast with the four color theorem for the plane.) de Bruijn torus
In combinatorial mathematics, a de Bruijn torus is an array of symbols from an alphabet (often just 0 and 1) that contains every m-by-n matrix exactly once. It is a torus because the edges are considered wraparound for the purpose of finding matrices. Its name comes from the De Bruijn sequence, which can be considered a special case where n is 1 (one dimension).
The torus can also be described as a quotient of the Cartesian plane under the identifications

  
    
      
        (
        x
        ,
        y
        )
        ∼
        (
        x
        +
        1
        ,
        y
        )
        ∼
        (
        x
        ,
        y
        +
        1
        )
        ,
        
      
    
    {\displaystyle (x,y)\sim (x+1,y)\sim (x,y+1),\,}
  or, equivalently, as the quotient of the unit square by pasting the opposite edges together, described as a fundamental polygon ABA−1B−1.