The planck unit is the smallest conceptual unit. It exists at such extremes that are difficult to verify directly, but in thought we can use it as the smallest whole number.
Thus a 2d scalar field consisting of only integer values is a tiled hexagonal lattice at which the points of intersection are the vertexes. What becomes very interesting is that math doesn't work the same way. A wavelength of 2 is not equal to two wavelengths of 1, even if the two can, along one ray, regularly intersect. Two halfs to not equal a whole. Classic concepts of math as a physical dimension do not work the same way. You can't add, only compare the two at any given point in a lattice.