We investigate the ordering of voter model on fractal lattices: Sierpinski Carpets and Sierpinski Gasket. We obtain a power law ordering, similar to the behavior of one-dimensional system, regardless of fractal ramification.

Many real networks share three generic properties: they are scale-free, display a small-world effect, and show a power-law strength-degree correlation. In this paper, we propose a type of deterministically growing networks called Sierpinski networks, which are induced by the famous Sierpinski fractals and constructed in a simple iterative way. We derive analytical expressions for degree distrib...

In this paper a simple scheme of map colour is introduced for the colour rendering of IFS fractals. The way of incorporating it into Barnsley's random iteration and versions of Hutchinson's deterministic algorithm is detailed. Examples are presented showing an elegant stylised colouring of such fractals as the Barnsley Fern and the Sierpinski gasket that provide attractive motifs for visualizat...

The paper is focused on how chaotic patterns, occurring in nature, might be used by biological 7 organisms to perform computations. This issue is investigated in the context of neural systems. As a simple model of chaotic patterns, the world of Sierpinski triangles is analysed. The paper 9 introduces the Sierpinski basis functions and the Sierpinski brain, which is able to perform classi)cation...

The article mainly studies the contracting similarity fixed point and the structure of the general Sierpinski gasket. Firstly, the paper analyzes the importance of contracting similarity fixed point in fractal geometry. Based on a series of definitions, the article studies the contracting similarity fixed point. Then, the paper researches on the structure of the general Sierpinski gasket, and d...

The numerical analysis of highly iterated Sierpinski microstrip patch antennas by method of moments (MoM) involves many tiny subdomain basis functions, resulting in a very large number of unknowns. The Sierpinski pre-fractal can be defined by an iterated function system (IFS). As a consequence, the geometry has a multilevel structure with many equal subdomains. This property, together with a mu...

The lattice fractal Sierpinski carpet and the percolation theory are applied to develop a new random stock price for the financial market. Percolation theory is usually used to describe the behavior of connected clusters in a random graph, and Sierpinski carpet is an infinitely ramified fractal. In this paper, we consider percolation on the Sierpinski carpet lattice, and the corresponding finan...

We will kill the old Luzin and Sierpinski sets in order to build a model where U (M) = U (N) = ℵ 1 and there are neither Luzin nor Sierpinski sets. Thus we answer a question of J. Steprans, communicated by S. Todorcevic on route from Evans to MSRI.

Localization due to space structure, rather than due to randomness, is investigated by studying the usual tight-binding model on the Sierpinski gasket. Some exact results are obtained from the decimation —renormalization-group method. It is surprising that there exist an infinite number of extended states on the Sierpinski gasket. This set of extended states forms a Cantor set. The rest of the ...