The behavior of exchange rate in various exchange markets is not seemingly predictable, while there are different forecasting methods to do so. One of these methods is to use fractals to identify exchange rate behavior. This paper has made attempts to explore the properties of fractals in Iran’s exchange market in order to it can predict and analyze the trend of exchange rate. Accordingly, th...

We describe relation between analysis on fractals and the theory of self-similar groups. In particular, we focus on the construction of the Laplacian on limit sets of such groups in several concrete examples, and in the general p.c.f. case. We pose a number of open questions.

Riesz potentials and Laplacian of fractal measures in metric spaces are introduced. They deene self{adjoint operators in the Hilbert space L 2 () and the former are shown to be compact. In the euclidean case the corresponding spectral asymptotics are derived by Besov space methods. The inverses of the Riesz potentials are fractal pseudo-diierential operators. For the Laplace operator the spectr...

A novel type of fractals (i.e., Zhang fractals) is yielded via solving time-varying or static nonlinear equations in complex domain by discrete-time complex-valued Zhang dynamics (DTCVZD). The DTCVZD model that uses different types of activation functions can generate various Zhang fractals. These fractals are different from the conventional Newton fractals discovered 30 years ago (since 1983) ...

Deterministic and random fractals, within the framework of Iterated Function Systems, have been used to model and study a wide range of phenomena across many areas of science and technology. However, for many applications deterministic fractals are locally too similar near distinct points while standard random fractals have too little local correlation. Random fractals are also slow and difficu...

A scale-invariant theory is derived for the linear optical properties of nontrivial fractals (fractal clusters) in the collective region, i.e., near the center of the absorption band. A model of dilute fractals is introduced and is used to find the shape of the wings of the absorption line in the binary approximation. Strong fluctuations of the local fields in nontrivial fractals are described....

We explore in depth the theory behind deterministic fractals by investigat­ ing transformations on metric spaces and the contraction mapping theorem. In doing so we introduce the notion of the Hausdorff distance metric and its connection to the space of fractals. In order to understand how deterministic fractals are generated, we develop the concept of an iterated function system (IFS) and what...

Many biological processes and objects can be described by fractals. The paper uses a new type of objects – blinking fractals – that are not covered by traditional theories considering dynamics of self-similarity processes. It is shown that both traditional and blinking fractals can be successfully studied by a recent approach allowing one to work numerically with infinite and infinitesimal numb...

Fractals are self-similar images. There are many techniques for generating fractals. IFS are one of them. IFS use a set of linear transformations for generation of fractals. We propose a method of modifying IFS such that non-linear transformations can be used for generating pleasant looking fractals. We also show a technique which ensures convergence of the fractal Images. Non-linear fractals h...