Related papers: Fractal dimension, and the problems traps of its e…
We study fractal measures on Euclidean space through the dynamics of "zooming in" on typical points. The resulting family of measures (the "scenery"), can be interpreted as an orbit in an appropriate dynamical system which often…
In this paper we first show that the usual three dimensionality of space, which is taken for granted, results from the spinorial behaviour of Fermions, which constitute the material content of the universe. It is shown that the resulting…
We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
The incomplete statistics for complex systems is characterized by a so called incompleteness parameter $\omega$ which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the…
In the last years there has been a growing interest in the understanding a vast variety of scale invariant and critical phenomena occurring in nature. Experiments and observations indeed suggest that many physical systems develop…
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study…
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…
Complex-dynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution of arbitrary interaction problem (physics/0305119,…
In this paper, a new concept, i.e. ultra-chaos, is proposed for the first time. Unlike a normal-chaos, statistical properties such as the probability density functions (PDF) of an ultra-chaos are sensitive to tiny disturbances. We…
We discuss properties of random fractals by means of a set of numbers that characterize their universal properties. This set is the generalized singularity specturm that consists of the usual spectrum of mulitfractal dimensions and the…
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
Data science is creating very exciting trends as well as significant controversy. A critical matter for the healthy development of data science in its early stages is to deeply understand the nature of data and data science, and to discuss…
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…
Uncertainty, characterised by randomness and stochasticity, is ubiquitous in applications of evolutionary game theory across various fields, including biology, economics and social sciences. The uncertainty may arise from various sources…
The possibility of complicated dynamic behaviour driven by non-linear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility…
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…
Understanding how size influences the internal characteristics of a system is a crucial concern across various fields. Concepts like scale invariance, universalities, and fractals are fundamental to this inquiry and find application in…
The structure of the large scale distribution of the galaxies have been widely studied since the publication of the first catalogs. Since large redshift samples are available, their analyses seem to show fractal correlations up to the…
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…