New Features on Gradient Pattern Analysis of Extended Complex Systems

Quantitative characterization of spatio-temporal patterns is clearly essential to the understanding of spatio-temporal phenomena. An important question in this problem concerns the long-term evolution of the pattern properties. Usually, the classical measures of complex extended variability do not take into account the directional information contained in a vectorial field: the main source of spatio-temporal variability. Moreover, since spatio-temporal information is even more accessible through high resolution digitized images, the need for sensitive techniques working in the real space is evident In this context, Gradient pattern analysis (GPA)[1] is a geometric computing method for characterizing geometrical bilateral symmetry breaking of an ensemble of symmetric vectors regularly distributed in a square lattice. The measures obtained from GPA are based on the spatio-temporal correlations between large and small amplitude fluctuations of the structure represented as a dynamical gradient pattern. By means of four gradient moments it is possible to quantify the relative fluctuations and scaling coherence at a dynamical numerical lattice and this is a set of proper measures of the pattern complexity and equilibrium. Taking into account massive gradient fields ($N>10?{4}$ vectors) In this talk we describe new features on how to compute the gradient moments based only on the phase portrait of bilateral symmetry breaking computed into the GPU/CUDA paradigm. Examples of this new approuch for big data is performed on Chaotic Coupled Map Lattices and also on gravitational N-body systems for cosmological large structure formation.

[1] Rosa et al. Physica A, 386:366-673, 2007. $doi:10.1016/j.physa.2007.08.044$