Entropic descriptor of a complex behaviour

We propose a new type of entropic descriptor that is able to quantify the statistical complexity (a measure of complex behaviour) by taking simultaneously into account the average departures of a system’s entropy S from both its maximum possible value S_max and its minimum possible value S_min. When these two departures are similar to each other, the statistical complexity is maximal. We apply the new concept to the variability, over a range of length scales, of spatial or grey-level pattern arrangements in simple models. The pertinent results confirm the fact that a highly non-trivial, length scale dependence of the entropic descriptor makes it an adequate complexity measure, able to distinguish between structurally distinct configurational macrostates with the same degree of disorder, a feature that makes it a good tool for discerning structures in complex patterns.