Entropic analysis of evolving 2-dimensional scalar fields: Field-dependent MFM datasets and non-local random-switch hysteresis

Different means of applying numerical techniques are proposed, typically used for pattern recognition purposes and for artificial texture classification and segmentation, to study the evolution of magnetization at the nano- and micro-scale in ferromagnetic samples. This framework is applied both to the Magnetic Force Microscope (MFM) dataset and to synthetic binary patterns of 2-dimensional spins, based on a nucleation and growth model for the hysteresis. In general 2-dimensional gray-scale frames carry information characterized by a spatial correlation between each pixel. Multiple datasets as the one analyzed, either 256-bit-valued magnetic field dependent MFM matrices or 2-bit-valued synthetic field dependent scatter matrices, are arranged as multidimensional arrays and their 2-dimensional entropy is computed.