Characterization of asymmetric fragmentation patterns in spatially extended systems

Spatially extended systems yield complex patterns arising from the coupled dynamics of its different regions. In this paper we introduce a matrix comp utational operator, F-A, for the characterization of asymmetric amplitude f ragmentation in extended systems. For a given matrix of amplitudes this ope ration results in an asymmetric-triangulation field composed by L points an d I straight lines. The parameter (I - L)/L is a new quantitative measure o f the local complexity defined in terms of the asymmetry in the gradient fi eld of the amplitudes. This asymmetric fragmentation parameter is a measure of the degree of structural complexity and characterizes the localized reg ions of a spatially extended system and symmetry breaking along the evoluti on of the system. For the case of a random field, in the real domain, which has total asymmetry, this asymmetric fragmentation parameter is expected t o have the highest value and this is used to normalize the values for the o ther cases. Here, we present a detailed description of the operator F-A and some of the fundamental conjectures that arises from its application in sp atio-temporal asymmetric patterns.