Complex networks modeled on the Sierpinski gasket

On the packing measure of the Sierpinski gasket

“…Thus, for every 0 < t d 2 which proves (23) and (22), provided that (21) holds. To conclude the proof there remains to show (21).…”

“…where K k is given by (18). Next, we show the existence of y 2 A k \ S 01 and z 2 A k nS 2 satisfying (21), (22), and (23). We denote by T k the set of equilateral triangles having side length 2 k and containing the cylinder sets of generation k. That is, for all k 1,…”

“…Its particularly simple structure makes it a natural setting for testing and developing various mathematical and physical ideas, such as problems of fractal geometry, harmonic analysis, random walks and PDEs on fractals, networks, number theory, etc. ; see [1], [3]- [6], chapter 12 of [7], [8], [11], [13], [19]- [23], [35], [39] and the references therein. Its pattern of construction seems to occur naturally to the human mind, at least in artistic contexts.…”

A small-world and scale-free network generated by Sierpinski Pentagon

“…Zhang et al [10,11,12] use the Sierpinski gasket to construct evolving networks which follow the power-law degree distribution and possess small-world effect. Several complex networks are modeled on self-similar fractals, for example, Apollonian networks [13], Koch networks [14,15,16,17,18], Platonic solids networks [19], Vicsek networks [20], Sierpinski networks [21,22], the hierarchical networks [23] and generalized self-similar networks [24].…”

Durer‐pentagon‐based complex network

“…Liu and Kong [15] researched Koch curve networks. Le et al [16] studied Sierpinski carpet‐based complex networks. However, these studies did not prove the fractal nature of the networks studied, and the dimensions of basic structures of the above models were small.…”