Fractals, Graphs and Neural Networks: The Holly Trinity of Nanostructures - An Overview and Comparison of Methods

Abstract

There are a lot of recently published research papers regarding representing nanostructures and biomimetic materials, using simple but powerful mathematical methods. In most of them, fractal theory, graph theory and neural networks are used. Having in mind variety of those methods, but in the same time complementarity and compatibility, they became very useful tool, and we named it “Holly Trinity” of mathematical approach in nanostructures. In this research we give an overview on interesting results in modelling nanostructures and their electrochemical and magnetic parameters, using those very actual and “easy to use” methods: fractal theory, graph theory and neural networks. We also compare them, in order to conclude about areas of their most useful applications.