This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we an...

Fractals, shapes comprised of self-similar parts, are not merely prescribed linear structures. A wide class of fractals can also arise from the rich dynamics inherent to nonlinear optics. I n 1967, Benoit Mandelbrot published a paper that gave birth to the study of fractals, entitled " How long is the coast of Britain? Statistical self similarity and fractional dimension " 1. According to Mande...

Popcorn fractals are instances of Integrated Fractal Systems involving trigonometric functions. In this paper, we study the effect of spherical, swirl and pseudo-horseshoe functions on popcorn fractals to produce talismanic and tantric designs. General Terms Fractal, Algorithm, Turbo C++, Program.

We show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution from a single input soliton.

Fractals are ubiquitous in nature and they are also useful in many modern applications because they are able to incorporate multiple length scales within the same material. However, the bottom-up construction of fractals has been difficult because the physico-chemical principles that underpin the fractal formation have remained elusive. Here, an experimental model setup was used to investigate ...

Daryl H. Hepting School of Computing Science Simon Fraser University Burnaby, British Columbia CANADA V5A IS6 e-mail: darylh@cs .sfu .ca The study of linear fractals has gained a great deal from the study of quadratic fractals , despit e important differences. Methods for classifying points in the complement of a fractal shape were originally dev elop ed for quadratic fractals , to provid e ins...

Efficiently controlling the trapping process, especially the trapping efficiency, is central in the study of trap problem in complex systems, since it is a fundamental mechanism for diverse other dynamic processes. Thus, it is of theoretical and practical significance to study the control technique for trapping problem. In this paper, we study the trapping problem in a family of proposed direct...

The recent development of analysis on fractal spaces is physically motivated by the study of diffusion in disordered media. The natural questions that arise concern the existence and uniqueness of a suitable Laplace operator, and the behaviour of the associated heat semigroup, on a space which is fractal. The classes of fractals for which these questions were ®rst answered were classes of exact...

Fractals are measurable metric sets with non-integer Hausdorff dimensions. If electric and magnetic fields are defined on fractal and do not exist outside of fractal in Euclidean space, then we can use the fractional generalization of the integral Maxwell equations. The fractional integrals are considered as approximations of integrals on fractals. We prove that fractal can be described as a sp...

We study derivations and Fredholm modules on metric spaces with a Dirichlet form. In particular, on finitely ramified fractals, we show that there is a non-trivial Fredholm module if and only if the fractal is not a tree. This result relates Fredholm modules and topology, and refines and improves known results on p.c.f. fractals.