A planar floor covering is formed having a top face and a bottom face opposite the top face, a length, a width perpendicular to the length, a top surface, a bottom surface opposite the top surface, a height between the top surface and the bottom surface, and physical properties or characteristics that vary across at least one of the length, the width and the height. The physical properties or characteristics include material composition, weight, density, directionality, stiffness, compressibility, elasticity and thickness.