Gradient pattern analysis: Difference between revisions

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'''Gradient pattern analysis''' ('''GPA''')<ref name=rosa2000>Rosa, R.R., Pontes, J., Christov, C.I., Ramos, F.M., Rodrigues Neto, C., Rempel, E.L., Walgraef, D. ''Physica A'' '''283''', 156 (2000).</ref> is 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 x M'' square amplitude [[matrix (mathematics)|matrix]]. An important property of the gradient representation is the following: A given ''M x M'' matrix where all amplitudes are different results in an ''M x M'' gradient lattice containing <math>N_{V} = M^2</math> asymmetric vectors. As each vector can be characterized by its norm and phase, variations in the <math>M^2</math> amplitudes can modify the respective <math>M^2</math> gradient pattern.

The original concept of GPA was introduced by Rosa, Sharma and Valdivia in 1999<ref name=Rosa99>Rosa, R.R.; Sharma, A.S.and Valdivia, J.A. ''Int. J. Mod. Phys. C'', '''10''', 147 (1999), [[doi:10.1142/S0129183199000103]].</ref>. Usually GPA is applied for spatio-temporal pattern analysis in physics and environmental sciences operating on time-series and digital images.