Related papers: Dynamics Motivated by Sierpinski Fractals
The problem of determining the underlying dynamics of a system when only given data of its state over time has challenged scientists for decades. In this paper, the approach of using machine learning to model the updates of the phase space…
Fractal geometry is a fundamental approach for describing the complex irregularities of the spatial structure of point patterns. The present research characterizes the spatial structure of the Swiss population distribution in the three…
Fractals are ubiquitous in the natural world, and their connection with phase transitions has been widely observed. This study investigates mechanisms of fractal formation from the perspective of phase transitions. A novel set of…
Development generating diffraction-related valuable expressions and formulas capable of initiating new era for diffraction and for scientific domains that use it provided. The main expression, among these, gives diffracted intensity as…
The question of a possible excitation and emergence of fractional type dynamics, as a more realistic framework for understanding emergence of complex systems, directly from a conventional integral order dynamics, in the form a continuous…
The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…
Cabrelli, Forte, Molter and Vrscay in 1992 considered a {fuzzy} version of the theory of iterated function systems (IFSs in short) and their fractals%The idea was to extend the classical Hutchinson-Barnsley operator to selfmaps of a metric…
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 percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
Compelling evidence exists to show that the structure of molecular clouds is fractal in nature. In this paper, the author reiterates this view and, in addition, asserts that not only is cloud geometry fractal, but that they also have a…
In nature, there are many phenomena with both irregularity and uncertainty. Therefore, a fuzzy-valued fractal interpolation is more useful for modeling them than fuzzy interpolation or fractal interpolation. We construct fractal…
We investigate the iterative construction of discrete Laplacians on 2D square lattices, revealing emergent fractal-like patterns shaped by modular arithmetic. While classical 2222-style iterations reproduce known structures such as the…
We study the dynamics of a generic endomorphism $f$ of an Oka-Stein manifold $X$. Such manifolds include all connected linear algebraic groups and, more generally, all Stein homogeneous spaces of complex Lie groups. We give several…
We study here the semiclassical dynamics of a superconducting circuit constituted by two Josephson junctions in series, in the presence of a voltage bias. We derive the equations of motion for the circuit through a Hamiltonian description…
Using Caputo fractional derivative of order $\alpha $ we build the fractional jet bundle of order $\alpha $ and its main geometrical structures. Defined on that bundle, some fractional dynamical systems with applications to economics are…
Many geo-engineering applications, e.g., enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase-field…
The dynamic and kinetic behavior of processes occurring in fractals with spatial discrete scale invariance (DSI) is considered. Spatial DSI implies the existence of a fundamental scaling ratio (b_1). We address time-dependent physical…
The Josephson effect is a hallmark signature of the superconducting state, which, however, has been sparsely explored in non-crystalline superconducting materials. Motivated by this, we consider a Josephson junction consisting of two…
A feasible model is introduced that manifests phenomena intrinsic to iterative complex analytic maps (such as the Mandelbrot set and Julia sets). The system is composed of two coupled alternately excited oscillators (or self-sustained…
It has been shown that the Sierpi\'nski gasket-like sets can appear as the Julia sets of some geometrically finite rational maps. In this paper we prove that such type of Julia sets can also appear in the rational maps containing Siegel…