The Law of Emergence of Self-similar Structures in Complex Systems and Complex Networks

In the real world,tree fractal structure exists in wide-spreading complex systems.Recently,the exploring of complex networks reveals that a vast amount of complex networks possess self-similar structure.The subsequent question is how the self-similar structure is formed and what the evolving process is.In this paper,considering both the complex systems and complex networks,we present a model of growing tree.From the argumentations given by this model,it shows that the evolving process and the emergence of self-similar structure can be completely expounded by a simple exponent law.This law is the self-organized critical state which governs the ordered evolving process and leads to the emergence of the layer-by-layer similar structure.The dimension of the tree fractal or the similar exponent is a measure of the function of system.Complexity resides in simplicity.The simple power law implies all of the information of the self-organized evolving process and the emergence of similar structure.It is an universal dynamics to govern the wide phenomena in the real world.