The shape of the density kernel should match the fractal nature of the iterative USM function itself. The solution reported here will first be described for a USM coordinate, and illustrated for an arbitrary coordinate of the map, say the horizontal dimension of the forward map in Figure 1. The value, K, of the proposed Kernel function (Equation 2) in map coordinate position u, has two user-defined parameters, memory length, L, and smoothing, S, which is the ratio between the areas assigned to two consecutive Markov orders (e.g. S = 2 implies the kernel density area assigned to order i ≤ L-1 is twice the area assigned to order i-1).