Related papers: Micro and Macro Fractals generated by multi-valued…
A type of fractal dimension definition is based on the generalized entropy function. Both entropy and fractal dimension can be employed to characterize complex spatial systems such as cities and regions. Despite the inherent connect between…
In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and…
Correlation functions of CFT operators with infinite scaling dimension are rich, multifaceted objects that describe physics ranging across classical holography, black hole dynamics, and flat-space scattering amplitudes. In this work, we…
A finite universe naturally supports chaotic classical motion. An ordered fractal emerges from the chaotic dynamics which we characterize in full for a compact 2-dimensional octagon. In the classical to quantum transition, the underlying…
In this paper we study the Hutchinson-Barnsley theory of fractals in the setting of multimetric spaces (which are sets endowed with point separating families of pseudometrics) and in the setting of topological spaces. We find natural…
We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…
We introduce a class of flat currents with fractal properties, called fractional currents, which satisfy a compactness theorem and remain stable under pushforwards by H\"older continuous maps. In top dimension, fractional currents are the…
The fractal cosmological model which accounts for observable fractal properties of the Universe's large-scale structure is constructed. In this framework these properties are consequences of the rotary symmetry of charged scalar meson…
Several studies have investigated the fractal and multifractal nature of magnetic features in the solar photosphere and its variation with the solar magnetic activity cycle. Here we extend those studies by examining the fractal geometry of…
This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its…
We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…
Perfect fractals are mathematical objects that, because they are generated by recursive processes, have self-similarity and infinite complexity. In particular, they also have a fractional dimension. Although several proposals for the study…
The optical spectra of fractal multilayer dielectric structures have been shown to possess spectral scalability, which has been found to be directly related to the structure's spatial (geometrical) self-similarity. Phase and amplitude…
Linear and nonlinear dissipative structures emerge in the irradiated single and multi walled carbon nano-tubes in the form of collision cascades and thermal spikes. These are diagnosed by the information theoretic tools of fractal dimension…
We consider cosmological models based on the spectral action formulation of (modified) gravity. We analyze the coupled effects, in this model, of the presence of nontrivial cosmic topology and of fractality in the large scale structure of…
The concept of multifractality offers a powerful formal tool to filter out multitude of the most relevant characteristics of complex time series. The related studies thus far presented in the scientific literature typically limit themselves…
Since the recent dissertation by Steffen Winter, for certain self-similar sets $F$ the growth behaviour of the Minkowski functionals of the parallel sets $F_\varepsilon := \{x\in \mathbb R^d : d(x,F)\leq \varepsilon\}$ as $\varepsilon…
We establish pointwise and distributional fractal tube formulas for a large class of compact subsets of Euclidean spaces of arbitrary dimensions. These formulas are expressed as sums of residues of suitable meromorphic functions over the…
The relation between critical exponents, characterizing a continuous phase transition, and the fractal structure of physical lines, proliferating at the critical point, is established by considering the two-dimensional O($N$) spin model for…
Quantum spin networks overcome the challenges of traditional charge-based electronics by encoding the information into spin degrees of freedom. Although beneficial for transmitting information with minimal losses when compared to their…