A method to discern complexity in two-dimensional patterns generated by coupled map lattices

Comparison of SDL and LMC measures of complexity: Atoms as a testbed

“…the distance from its actual state to equilibrium [6,7] defined for a discrete probability distribution {p i } as follows [6] (22)…”

“…According to [5][6][7] S and D are the two basic ingredients for calculating complexity. In our 3-dimensional case, we employ instead of (25) the formula…”

“…In contrast, there is a class of definitions of complexity, which can be calculated easily i.e. the simple measure of complexity Γ α,β according to Shiner, Davison, Landsberg (SDL) [4], and the statistical measure of complexity C, defined by López-Ruiz, Mancini, Calbet (LMC) [5][6][7].…”

Statistical Complexity. Applications in Electronic Systems

“…The most important point is that the new definition successfully enables us to discern situations regarded as complex. For example, we have performed different applications in complex systems with some type of discretization: one of them was the study of this magnitude in a phase transition in a coupled map lattice [21] and the other one was its calculation for the time evolution of a discrete gas out of equilibrium [22]. Other applications to more realistic systems can also be found in the literature, see for instance this major reference which is the only monograph published on the topic of statistical complexity applied …”

Self-synchronization of Cellular Automata: An Attempt to Control Patterns

“…A method to detect this kind of transition, based in the calculation of a statistical measure of complexity for patterns, has been proposed in the Refs. [4].…”