This is a pedagogical review of the subject of linear polymers on deterministic finitely ramified fractals. For these, one can determine the critical properties exactly by real-space renormalization group technique. We show how this is used to determine the critical exponents of self-avoiding walks on different fractals. The behavior of critical exponents for the n-simplex lattice in the limit ...

G.Geetha Professor and Head, Division of Research and Development Lovely Professional University, Phagwara, India [email protected] Abstract We propose the fractal generation method to generate the different types of fractals using chaos theory. The fractals are generated by Iterated Function System (IFS) technique. The chaos theory is an unpredictable behavior arises in the dynamical system...

The study of linear fractals has gained a great deal from the study of quadratic fractals, despite important dierences. Methods for classifying points in the complement of a fractal shape were originally developed for quadratic fractals, to provide insight into their underlying dynamics. These methods were later modied for use with linear fractals. This paper reconsiders one such classication, ...

In this paper, we consider the strict self-assembly of fractals in one of the most well-studied models of tile based self-assembling systems known as the Two-handed Tile Assembly Model (2HAM). We are particularly interested in a class of fractals called discrete self-similar fractals (a class of fractals that includes the discrete Sierpinski’s carpet). We present a 2HAM system that strictly sel...

We introduce an alternative coordinate system based on derivative polar and spherical coordinate functions and construct a root-to-canopy analytic formulation for tree fractals. We develop smooth tree fractals and demonstrate the equivalence of their canopies with iterative straight lined tree fractals. We then consider implementation and application of the analytic formulation from a computati...

We consider a class of Gibbs measures on self-affine Sierpinski carpets and perform the multifractal analysis of its elements. These deterministic measures are Gibbs measures associated with bundle random dynamical systems defined on probability spaces whose geometrical structure plays a central rôle. A special subclass of these measures is the class of multinomial measures on Sierpinski carpet...

We construct a linear extension operator Π that extends a function u defined on a Sierpinski gasket S which satisfies the Hölder estimate |u(x)− u(y)| ≤ C0|x− y| for all x, y on S, to a larger domain Ω ⊆ R. The extension function Πu is defined everywhere in Ω, is Hölder continuous everywhere in Ω, corresponds with u at every point on S and satisfies the estimate |Πu|Ω,β ≤ C‖u‖S,β with a constan...

Fractal theory has been used widely for studying the scaling properties of different biological and ecological time series [1-3]. A phenomenon showinga repeating pattern at every scale is called fractal [4]. Fractals can be regular or complex [5]. In fact, fractal objects can be characterized using a scaling exponent that is called fractal dimension. Regular and complex fractals have integer an...