JPD-Coloring of the Monohedral Tiling for the Plane

Abstract

We introduce a definition of coloring by using joint probability distribution “JPD-coloring” for the plane which is equipped by tiling $\mathfrak{I}$. We investigate the JPD-coloring of the r-monohedral tiling for the plane by mutually congruent regular convex polygons which are equilateral triangles at r = 3 or squares at r = 4 or regular hexagons at r = 6. Moreover we present some computations for determining the corresponding probability values which are used to color in the three studied cases by MAPLE-Package.