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Abstract
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In recent years, the investigation of two dimensional phenomena has been frequently considered, in literatures. In general, the study of such phenomena is a very difficult, due to their complex dynamics. However, many of them possess various universal characteristics such as fractality that has increased the possibility of prediction and also better understanding of their governing dynamics. Generally, these phenomena are not easily understandable, due to their inherent complexity. To study them, various novel methods have been introduced. One of them, is to map an image into a network. By investigating the properties of the resulting network, one is able to extract the properties of the original image. In this these, we study two dimensional fractal phenomena by using two dimensional visibility graph theory. In this respect, we use two prominent fractals, i.e., fractional Gaussian noise and fractional Brownian motion, both are simulated by computer. After mapping images into visibility graphs, a number of most famous and important topological characteristics of the resulting graphs are calculated: such as average degree, standard deviation of degrees, clustering, assortativity, maximum eigenvalue of the adjacency matrix and also degree distribution. Since, we know about the inherent dynamics of simulated fractal series, then by finding the similarity between a real world image and a simulated fractal one, we can achieve a better understanding of that real image. Many methods have been proposed for doing such analysis, but for the first time, we use the visibility graph theory which is a novel approach.
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