Gradient pattern analysis: Difference between revisions

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== Introduction ==

%Gradient Pattern Analysis (texto principal)

The {\it''Gradient gradientPattern pattern analysis}Analysis'' (GPA) (\cite{rosa2000},\cite{rosa03}) basically consists in a geometric computing method for characterizing symmetry breaking of an ensemble of asymmetric vectors regularly distributed in a square lattice. Usually, the lattice of vectors represent the first-order gradient of a scalar field, here an $M\times M$ square amplitude matrix. An important property of the gradient representation is the following: A given $M\times M$ matrix where all amplitudes are different results a

$M\times M$ gradient lattice containing $N_{V}=M^{2}$ asymmetric vectors. As each vector can be characterized by its norm and phase, variations in the $M^{2}$ amplitudes can modify the respective $M^{2}$ gradient pattern.