Probability distance measures applied to analyze response to stochasticity in R8 cell point pattern formation.

(a)-(b) are generated using the fidelity, F, and (c)-(d) using the Kolmogorov distance, K, for nearest neighbor distances and angles respectively. Stochasticity was introduced in the model through drawing the parameter Du and Ds in the differential equations Eqs 1–4 from a normal distribution with varying standard deviation, σ, and mean value, μ. The simulation results were compiled, and nearest R8 cell neighbor angle and distance distributions were obtained. Kolmogorov and fidelity of the resulting distributions where computed with reference to the perfect pattern case. Here, a value of 1 corresponds to a perfectly ordered pattern, and a value of 0 corresponds to a completely irregular pattern. This figure illustrates that the functional form is independent of the measure used.