Figure 2 illustrates how the choice of parameters will set both the resolution and detail of the pattern representation. If smoothing is set to +∞ then the kernel density will be distributed between the different fractions exactly as it would in a Markov transition matrix with the same memory length. This becomes clearer when a two dimension example is used such as the more familiar representation of nucleotide sequences. To illustrate this procedure, Equation 2 was applied to the forward map of a small nucleotide sequence represented in Figure 1, which results in the density distribution represented in Figure 3.