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The main goal of this paper has a double purpose. On the one hand, we propose a new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting…
This paper investigates a class of deterministic fractals whose construction is governed by arithmetic sequences. We introduce the essential fractal prime set P_{ess} , a variant of the Cantor set constructed using the sequence of prime…
It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we…
This article describes a new method of producing space filling fractal dragon curves based on a hinged tiling procedure. The fractals produced can be generated by a simple L-system. The construction as a hinged tiling has the advantage of…
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…
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…
We explore the fractal nature of particle showers using Monte-Carlo simulation. We define the fractal dimension of showers measured in a high granularity calorimeter designed for a future lepton collider. The shower fractal dimension…
In past decades, the application of fractals to electrode design for enhanced signaling and electrochemical performance was a popular subject and enabled the growth of consumer micro-electronics. Supercapacitors, which are energy storage…
Effective sequence modeling fundamentally requires balancing the retention of unbounded history with the high-resolution detection of abrupt short-term variations common in real-world phenomena. However, existing state space models (SSMs)…
The fractal and self-similarity properties are revealed in many real complex networks. However, the classical information dimension of complex networks is not practical for real complex networks. In this paper, a new information dimension…
The light scattering experiment establishes a relationship between refractive index fluctuations and fractal dimension in weakly scattering tissue-like media. Based on the box-counting approach, an analytical model is developed and shows…
We study the convergence of certain subseries of the harmonic series corresponding to increasing sequences of integers whose digits in a certain base are not uniformly distributed. We also discuss the case of irregular sequences, where the…
Topological Data Analysis (TDA) uses insights from topology to create representations of data able to capture global and local geometric and topological properties. Its methods have successfully been used to develop estimations of fractal…
The cosmic web is one of the most complex systems in nature, consisting of galaxies and clusters of galaxies joined by filaments and walls, leaving large empty regions called cosmic voids. The most common method of describing the web is a…
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…
Fractons are anyons classified into equivalence classes and they obey a specific fractal statistics. The equivalence classes are labeled by a fractal parameter or Hausdorff dimension $h$. We consider this approach in the context of the…
The foundation of the theory presented here has already been proved to be effective for the case of curves belonging to the Koch family. The present paper extends the investigation to more complex curves, namely randomly generated curves…
The scaling properties of spectra of real world complex networks are studied by using the wavelet transform. It is found that the spectra of networks are multifractal. According to the values of the long-range correlation exponent, the Hust…
A fractal method to detect, locate and quantify chaos in multi-dimensional-conservative-closed systems, based on the creation of artificial exits, is presented. The method is invariant under space-time changes of coordinates and can be used…
Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal…