Related papers: On the length of arcs in labyrinth fractals
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
Fractals, complex shapes with structure at multiple scales, have long been observed in Nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains and coastlines. With their highly polished…
Even though many objects and phenomena of importance in geophysics have been shown to have fractal character, there are still many of them which show self-similar character and yet to be studied. The objective of the present work is to…
In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension. This dimension stands out from the…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
The study of Lipschitz equivalence of fractals is a very active topic in recent years. Most of the studies in literature concern totally disconnected fractals. In this paper, using finite state automata, we construct a bi-Lipschitz map…
The thesis deals with recognizing diffeomorphisms from fractal properties of discrete orbits, generated by iterations of such diffeomorphisms. The notion of fractal properties of a set refers to the box dimension, the Minkowski content and…
The fractal structure with a power index of 2 is considered within the framework of the universe with the linear law of evolution. The fractal structure arises due to the linear evolution of the scale of mass. Potential fluctuations connect…
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…
We forge connections between the theory of fractal sets obtained as attractors of iterated function systems and process calculi. To this end, we reinterpret Milner's expressions for processes as contraction operators on a complete metric…
Following \cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimension of sets which can be defined in a recursive way and we…
The famous Laplace's Demon is not only of strict physical determinism, but also related to the power of differential equations. When deterministically extended structures are taken into consideration, it is admissible that fractals are…
We report an algorithm for the partition of a line segment according to a given ratio $\nu$. At each step the length distribution among sets of the partition follows a binomial distribution. We call $k$-set to the set of elements with the…
This paper uses a connection between bounded remainder sets in $\mathbb{R}^d$ and cut-and-project sets in $\mathbb{R}$ together with the fact that each one-dimensional Pisot substitution sequence is bounded distance equivalent to some…
We prove the existence of fractal solutions to a class of linear ordinary differential equations.This reveals the possibility of chaos in the very short time limit of the evolution even of a linear one dimensional dynamical system.
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
We build a multifractal object and use it as a support to study percolation. We identify some differences between percolation in a multifractal and in a regular lattice. We use many samples of finite size lattices and draw the histogram of…
Fractals are defined as geometric shapes that exhibit symmetry of scale. This simply implies that fractal is a shape that it would still look the same even if somebody could zoom in on one of its parts an infinite number of times. This…
In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our method is to establish some graph structures on fractal squares to reveal the…
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…