Related papers: Construction of Fractal Functions Using Kannan Map…
We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
We show that a fractal affine function $f(x)$ defined by a system $\mathcal S$ which does not satisfy weak separation property is a quadratic function.
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…
A mathematical method for constructing fractal curves and surfaces, termed the $p\lambda n$ fractal decomposition, is presented. It allows any function to be split into a finite set of fractal discontinuous functions whose sum is equal…
A novel method for constructing a nonlinear fractal histopolation function associated with a given histogram is introduced in this paper. In contrast to classical fractal interpolation methods, which produce continuous and interpolatory…
For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to…
Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical…
IFS fractals - the attractors of Iterated Function Systems - have motivated plenty of research to date, partly due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design…
In this paper are investigated strictly self-similar fractals that are composed of an infinite number of regular star-polygons, also known as Sierpinski $n$-gons, $n$-flakes or polyflakes. Construction scheme for Sierpinsky $n$-gon and…
There has been a significant effort in recent years to generalize the traditional concept of iterated function systems (IFS).In this article, we proposed Suzuki contraction in hyperspace and finding out the fixed point for Hutchinson…
The paper concerns fractal homeomorphism between the attractors of two bi-affine iterated function systems. After a general discussion of bi-affine functions, conditions are provided under which a bi-affine iterated function system is…
A new calculus on fractal curves, such as the von Koch curve, is formulated. We define a Riemann-like integral along a fractal curve F, called F-alpha-integral, where alpha is the dimension of F. A derivative along the fractal curve called…
Suppose a graph-directed iterated function system consists of maps f_e with upper estimates of the form d(f_e(x),f_e(y)) <= r_e d(x,y). Then the fractal dimension of the attractor K_v of the IFS is bounded above by the dimension associated…
The term fractal describes a class of complex structures exhibiting self-similarity across different scales. Fractal patterns can be created by using various techniques such as finite subdivision rules and iterated function systems. In this…
Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer…
By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…
In the first section we review recent results on the harmonic analysis of fractals generated by iterated function systems with emphasis on spectral duality. Classical harmonic analysis is typically based on groups whereas the fractals are…
This paper introduces Fourier duality for a class of affine iterated function systems (IFS) T_i. These systems are determined by a finite family of contractive affine maps in R^d. Our Fourier duality applies to the resulting probability…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…