Studying the fractal properties of Ceres

Abstract Currently, the asteroid Ceres belongs to small celestial bodies with the most well-known physical parameters. The study of the structural and real properties of Ceres is an urgent and modern task, the solution of which will make it possible to develop the evolutionary theory of a minor planet. In this work, the fractal properties of the dwarf planet Ceres were analyzed using data from the Dawn space mission. Using the expansion in a harmonic series in spherical functions the height parameters of the structural model of Ceres, a 3D model of Ceres was constructed. The analysis showed that the resulting system has a complex multiparameter fractal configuration. The study of such objects requires the use of harmonic multiparameter methods. Multivariate fractal analysis allows to represent systems similar to the Ceres model in the form of a spectrum of fractal dimensions. The advantage of fractal analysis is the ability to explore local areas of the physical surface. In this work, the Minkowski algorithm was used for this purpose. At the final stage, an overdetermined system was solved for various local areas of topocentric information in order to postulate a model that takes into account external measures. Fractal dimensions D are determined for local regions and the entire model of the planet. Fractal dimensions vary from 1.37 to 1.92 depending on the longitude and latitude of Ceres. The main results are as follows: 1) the structure of the Ceres surface varies more strongly in longitude; 2) the structure of Ceres is smoother in latitude; 3) the coefficient of self-similarity changes rather quickly in longitude, which indicates that different local regions of the minor planet were formed under the influence of various physical processes. It is necessary to emphasize that the resulting fractal dimensions are significantly scattered both in longitude and latitude of Ceres. This fact confirms the presence of a complex structure in the spatial model of a minor planet. This also applies to the actual physical surface of Ceres. The results of the work allow us to conclude that fractal modeling can give independent values of the fractal dimension both for the entire model of Ceres and for its local macrostructural regions.

Download Full-text

DECODING OF HAND GESTURES BY FRACTAL ANALYSIS OF ELECTROMYOGRAPHY (EMG) SIGNAL

Fractals ◽

10.1142/s0218348x19500221 ◽

2019 ◽

Vol 27 (03) ◽

pp. 1950022 ◽

Cited By ~ 19

Author(s):

HAMIDREZA NAMAZI

Keyword(s):

Fractal Dimension ◽

Fractal Analysis ◽

Complex Structure ◽

Fractal Dimensions ◽

Major Research ◽

Hand Gestures ◽

Research Areas ◽

Emg Signal ◽

Human Movements ◽

Different Types

One of the major research areas in analysis of human movements is to investigate how different movements are related to biosignals. Hand gestures belong to major movements of human that have been considered widely by researchers. Therefore, decoding of different hand’s gestures by analysis of related biosignal is very important to be considered. In this paper, we analyze the complex structure of electromyography (EMG) signal from subjects who did eight hand gestures. For this purpose, we chose fractal dimension as the indicator of complexity. The analysis showed that the EMG signal has the greatest and lowest fractal dimensions in case of fingers flexed together in fist, and pointing index, respectively. The employed method in this research is not limited to the analysis of the influence of hand’s gestures on EMG signal. However, it can be widely applied to analyze the influence of different types of stimuli on different human’s biosignals.

Download Full-text

Structure characterization of ground calcium carbonate flocs by fractal analysis and their effects on handsheet properties

TAPPI Journal ◽

10.32964/tj12.3.17 ◽

2013 ◽

Vol 12 (3) ◽

pp. 17-23 ◽

Cited By ~ 3

Author(s):

WANHEE IM ◽

HAK LAE LEE ◽

HYE JUNG YOUN ◽

DONGIL SEO

Keyword(s):

Fractal Analysis ◽

Structural Characteristics ◽

Fractal Dimensions ◽

Strength Loss ◽

Structure Characterization ◽

Uniform Size ◽

Cross Sectional ◽

Floc Size ◽

Mass Fractal ◽

Handsheet Properties

Preflocculation of filler particles before their addition to pulp stock provides the most viable and practical solution to increase filler content while minimizing strength loss. The characteristics of filler flocs, such as floc size and structure, have a strong influence on preflocculation efficiency. The influence of flocculant systems on the structural characteristics of filler flocs was examined using a mass fractal analysis method. Mass fractal dimensions of filler flocs under high shear conditions were obtained using light diffraction spectroscopy for three different flocculants. A single polymer (C-PAM), a dual cationic polymer (p-DADMAC/C-PAM) and a C-PAM/micropolymer system were used as flocculants, and their effects on handsheet properties were investigated. The C-PAM/micropolymer system gave the greatest improvement in tensile index. The mass fractal analysis showed that this can be attributed to the formation of highly dense and spherical flocs by this flocculant. A cross-sectional analysis of the handsheets showed that filler flocs with more uniform size were formed when a C-PAM/micropolymer was used. The results suggest that a better understanding of the characteristics of preflocculated fillers and their influence on the properties of paper can be gained based on a fractal analysis.

Download Full-text

Architectural Bias in Recurrent Neural Networks: Fractal Analysis

Neural Computation ◽

10.1162/08997660360675099 ◽

2003 ◽

Vol 15 (8) ◽

pp. 1931-1957 ◽

Cited By ~ 13

Author(s):

Peter Tiňo ◽

Barbara Hammer

Keyword(s):

Neural Networks ◽

Fractal Analysis ◽

Recurrent Neural Networks ◽

Markov Models ◽

Fractal Dimensions ◽

Transition Diagram ◽

Activation Patterns ◽

Box Counting ◽

Fractal Clusters ◽

Finite State

We have recently shown that when initialized with “small” weights, recurrent neural networks (RNNs) with standard sigmoid-type activation functions are inherently biased toward Markov models; even prior to any training, RNN dynamics can be readily used to extract finite memory machines (Hammer & Tiňo, 2002; Tiňo, Čerňanský, &Beňušková, 2002a, 2002b). Following Christiansen and Chater (1999), we refer to this phenomenon as the architectural bias of RNNs. In this article, we extend our work on the architectural bias in RNNs by performing a rigorous fractal analysis of recurrent activation patterns. We assume the network is driven by sequences obtained by traversing an underlying finite-state transition diagram&a scenario that has been frequently considered in the past, for example, when studying RNN-based learning and implementation of regular grammars and finite-state transducers. We obtain lower and upper bounds on various types of fractal dimensions, such as box counting and Hausdorff dimensions. It turns out that not only can the recurrent activations inside RNNs with small initial weights be explored to build Markovian predictive models, but also the activations form fractal clusters, the dimension of which can be bounded by the scaled entropy of the underlying driving source. The scaling factors are fixed and are given by the RNN parameters.

Download Full-text

Graph fractal dimension and the structure of fractal networks

Journal of Complex Networks ◽

10.1093/comnet/cnaa037 ◽

2020 ◽

Vol 8 (4) ◽

Author(s):

Pavel Skums ◽

Leonid Bunimovich

Keyword(s):

Complex Networks ◽

Evolutionary Biology ◽

Real Life ◽

Fractal Dimensions ◽

Network Models ◽

Self Similarity ◽

Descriptive Complexity ◽

Network Communities ◽

Fractal Properties ◽

Continuous Objects

Abstract Fractals are geometric objects that are self-similar at different scales and whose geometric dimensions differ from so-called fractal dimensions. Fractals describe complex continuous structures in nature. Although indications of self-similarity and fractality of complex networks has been previously observed, it is challenging to adapt the machinery from the theory of fractality of continuous objects to discrete objects such as networks. In this article, we identify and study fractal networks using the innate methods of graph theory and combinatorics. We establish analogues of topological (Lebesgue) and fractal (Hausdorff) dimensions for graphs and demonstrate that they are naturally related to known graph-theoretical characteristics: rank dimension and product dimension. Our approach reveals how self-similarity and fractality of a network are defined by a pattern of overlaps between densely connected network communities. It allows us to identify fractal graphs, explore the relations between graph fractality, graph colourings and graph descriptive complexity, and analyse the fractality of several classes of graphs and network models, as well as of a number of real-life networks. We demonstrate the application of our framework in evolutionary biology and virology by analysing networks of viral strains sampled at different stages of evolution inside their hosts. Our methodology revealed gradual self-organization of intra-host viral populations over the course of infection and their adaptation to the host environment. The obtained results lay a foundation for studying fractal properties of complex networks using combinatorial methods and algorithms.

Download Full-text

Fractal Analysis of Morphological Parameters of the Structure Materials

10.30987/graphicon-2019-2-240-243 ◽

2019 ◽

Author(s):

Константин Макаренко ◽

Konstantin Makarenko ◽

Александр Никитин ◽

Alexander Nikitin

Keyword(s):

Elementary Particle ◽

Fractal Analysis ◽

Ductile Iron ◽

Crystallization Process ◽

Morphological Characteristics ◽

Fractal Dimensions ◽

Structural Materials ◽

Morphological Parameters ◽

Graphite Cell ◽

Mesh Method

It is proposed to use the methods of fractal analysis to determine the morphological characteristics of the structure of structural materials. The questions of fractal aggregation of particles in the process of crystallization of ductile iron are considered, an austenitic-graphite cell is used as an elementary particle. Based on the mesh method, images of the microstructure of ductile irons are analysed and conclusions are drawn about the similarity of the nature of the process of their crystallization and fractal aggregation of particles. Based on the calculated fractal dimensions, a theory is proposed to explain the features of the crystallization process of ductile irons.

Download Full-text

FRACTALS, NATURAL DISASTERS AND ECOLOGICAL PROBLEMS OF MALDIVES

10.32006/eeep.2018.2.1825 ◽

2018 ◽

pp. 18-25

Author(s):

Boyko Ranguelov ◽

Fathimath Shadiya

Keyword(s):

Local Population ◽

Fractal Dimensions ◽

Point Of View ◽

Negative Consequences ◽

Fractal Nature ◽

Fractal Properties ◽

Level Increase ◽

Ocean Level ◽

Ecological Problems ◽

Negative Phenomena

A new idea about the fractal nature of Maldives archipelago is under investigation. The origin of this famous Maldivian islands’ country is still questionable from geodynamic point of view. The present study is focused to the assessment of the fractal properties and the coefficients of the nonlinearity (fractal dimensions) of the areal spatial distribution of the major atolls of the Maldives. This is the most vulnerable area in the world from point of view of the global warming and the possible negative consequences to the country and population from the ocean level increase. From another side the natural hazards (tsunamis, storms, etc.) are common negative phenomena attacking the country. The strongly developed tourism – more than 30% of the GDP and the increased urbanization is another factor creating ecological problems to the local population. The relationships between the fractal nature and the possible ways to avoid the pollution are also in the focus of this research.

Download Full-text

PECULIARITIES OF THE RADIO SIGNALS AND HINDRANCES IN THE NAVIGATION SYSTEM OF THE REMOTE-PILOTED VEHICLES

Informatyka Automatyka Pomiary w Gospodarce i Ochronie Środowiska ◽

10.5604/01.3001.0010.8645 ◽

2018 ◽

Vol 8 (1) ◽

pp. 40-43 ◽

Cited By ~ 1

Author(s):

Mykola Mykyjchuk ◽

Volodymyr Markiv

Keyword(s):

Control System ◽

Fractal Analysis ◽

Navigation System ◽

Fractal Dimensions ◽

Vehicle Control ◽

Vital Role ◽

Environment Research ◽

Radio Signals

The article dwells upon the peculiarities of radio signals concerning the use of remote-piloted vehicles. It is highlighted that it is important take into consideration the fractal analysis of remote-piloted vehicles based on diverse fractal dimensions. The significance of remote-piloted vehicle control system investigation based on radio signals is presented. Also it is highlighted that there are many hindrances during the remote-piloted vehicle flight and it is important to take them into consideration and develop methods in order to omit them. Also the vital role of remote-piloted vehicles in different spheres of life, for example, in environment research is depicted.

Download Full-text

UV-Induced Fractal Surfaces

Fractals ◽

10.1142/s0218348x97000267 ◽

1997 ◽

Vol 05 (02) ◽

pp. 275-280 ◽

Cited By ~ 2

Author(s):

Cs. Beleznai ◽

R. Vajtai ◽

L. Nánai

Keyword(s):

Surface Morphology ◽

Structural Parameters ◽

Strong Dependence ◽

Pulsed Laser ◽

Fractal Dimensions ◽

Laser Source ◽

Physical Parameters ◽

Fractal Surfaces

Poly (tetrafluorethylene) and polyimide samples were irradiated by a pulsed laser source at 308 nm and the resulting surface morphology was investigated. The photoablated surfaces show a strong dependence on the optical and structural parameters of the polymers. The roughness of the fractal surfaces has been characterized by means of calculating their fractal dimensions and the results are interpreted as a function of the polymer physical parameters.

Download Full-text