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Fractal Fract
Special Issues
Fractal Geometry in Geospatial Data Analysis
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Fractal Geometry in Geospatial Data Analysis

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Geometry".

Deadline for manuscript submissions: closed (31 May 2021) | Viewed by 8674

Special Issue Editors

Prof. Dr. Mikolaj Karpinski

E-Mail Website
Guest Editor
Department of Computer Science and Automatics, University of Bielsko-Biala, 43-300 Bielsko-Biala, Poland
Interests: computer networks and wireless communication; computer security and cryptography; computing systems
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Svitlana Kuznichenko

E-Mail Website
Guest Editor
Department of Information Technologies, Odessa State Environmental University, 65016 Odessa, Ukraine
Interests: GIS analysis; GIS techniques; Big Data Analysis; MCDA; Fuzzy logic

Special Issue Information

Dear Colleagues,

Fractals are mathematical objects with fractional dimensions, as opposed to traditional, whole-dimensional shapes. Many structures have a fundamental property of geometric regularity known as scale invariance or self-similarity. Fractal geometry describes spatial forms more accurately and better than Euclidean geometry, allowing one to take into account the factors of randomness, chaos and unpredictability in modeling. Fractality is a convenient tool for describing and modeling processes and phenomena that generate structures that fully possess self-similarity properties and represent similar patterns at various spatial and temporal scales.

The geographic interpretation of fractals allows one to explore and solve complex problems in geospatial analysis, spatial modeling and spatial decision making. The development of the theoretical foundations of fractal geometry has contributed to the widespread use of fractals to describe various spatial phenomena in urban geography, urban morphology, landscape structure and transport networks.

The editorial team of Fractal and Fractional invites paper submissions of original research on applications of fractal geometry in geospatial data analysis. Suggested topics include, but are not limited to, the following:

  • A review of fractal geometry in geospatial data analysis;
  • Fractal geometry in the geospatial analysis of big data;
  • Fractal geometry in the geospatial analysis of urban models: urban morphology analysis, urban growth analysis, urban road network analysis, urban land use analysis, etc.;
  • The fractal analysis of remotely sensed images;
  • The development of software for fractal analysis in geographic information systems.

Prof. Dr. Mikolaj Karpinski
Prof. Dr. Svitlana Kuznichenko
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractal geometry
  • fractal dimension
  • geographic information systems
  • image analysis
  • data classification
  • pattern recognition
  • urban analysis

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Published Papers (3 papers)

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Research

14 pages, 2535 KiB  
Article
Particularities of Forest Dynamics Using Higuchi Dimension. Parâng Mountains as a Case Study
by Adrian Gabriel Simion, Ion Andronache, Helmut Ahammer, Marian Marin, Vlad Loghin, Iulia Daniela Nedelcu, Cristian Mihnea Popa, Daniel Peptenatu and Herbert Franz Jelinek
Fractal Fract. 2021, 5(3), 96; https://doi.org/10.3390/fractalfract5030096 - 13 Aug 2021
Cited by 7 | Viewed by 2035
Abstract
The legal or illegal losses and the natural disturbance regime of forest areas in Romania generate major imbalances in territorial systems. The main purpose of the current research was to examine the dynamics of the complexity of forests under the influence of forest [...] Read more.
The legal or illegal losses and the natural disturbance regime of forest areas in Romania generate major imbalances in territorial systems. The main purpose of the current research was to examine the dynamics of the complexity of forests under the influence of forest loss but also to compare the applicability of Higuchi dimension. In this study, two fractal algorithms, Higuchi 1D (H1D) and Higuchi 2D (H2D), were used to determine qualitative and quantitative aspects based on images obtained from a Geographic Information System (GIS) database. The H1D analysis showed that the impact of forest loss has led to increased fragmentation of the forests, generating a continuous increase in the complexity of forest areas. The H2D analysis identified the complexity of forest morphology by the relationship between each pixel and the neighboring pixels from analyzed images, which allowed us to highlight the local characteristics of the forest loss. The H1D and H2D methods showed that they have the speed and simplicity required for forest loss analysis. Using this methodology complementary to GIS analyses, a relevant status of how forest loss occurred and their impact on tree-cover dynamics was obtained. Full article
(This article belongs to the Special Issue Fractal Geometry in Geospatial Data Analysis)
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14 pages, 2208 KiB  
Article
Fat Tail in the Phytoplankton Movement Patterns and Swimming Behavior: New Insights into the Prey-Predator Interactions
by Xi Xiao, Caicai Xu, Yan Yu, Junyu He, Ming Li and Carlo Cattani
Fractal Fract. 2021, 5(2), 49; https://doi.org/10.3390/fractalfract5020049 - 25 May 2021
Cited by 1 | Viewed by 2055
Abstract
Phytoplankton movement patterns and swimming behavior are important and basic topics in aquatic biology. Heavy tail distribution exists in diverse taxa and shows theoretical advantages in environments. The fat tails in the movement patterns and swimming behavior of phytoplankton in response to the [...] Read more.
Phytoplankton movement patterns and swimming behavior are important and basic topics in aquatic biology. Heavy tail distribution exists in diverse taxa and shows theoretical advantages in environments. The fat tails in the movement patterns and swimming behavior of phytoplankton in response to the food supply were studied. The log-normal distribution was used for fitting the probability density values of the movement data of Oxyrrhis marina. Results showed that obvious fat tails exist in the movement patterns of O. marina without and with positive stimulations of food supply. The algal cells tended to show a more chaotic and disorderly movement, with shorter and neat steps after adding the food source. At the same time, the randomness of turning rate, path curvature and swimming speed increased in O. marina cells with food supply. Generally, the responses of phytoplankton movement were stronger when supplied with direct prey cells rather than the cell-free filtrate. The scale-free random movements are considered to benefit the adaption of the entire phytoplankton population to varied environmental conditions. Inferentially, the movement pattern of O. marina should also have the characteristics of long-range dependence, local self-similarity and a system of fractional order. Full article
(This article belongs to the Special Issue Fractal Geometry in Geospatial Data Analysis)
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14 pages, 4337 KiB  
Article
Image Compression Using Fractal Functions
by Olga Svynchuk, Oleg Barabash, Joanna Nikodem, Roman Kochan and Oleksandr Laptiev
Fractal Fract. 2021, 5(2), 31; https://doi.org/10.3390/fractalfract5020031 - 14 Apr 2021
Cited by 25 | Viewed by 3108
Abstract
The rapid growth of geographic information technologies in the field of processing and analysis of spatial data has led to a significant increase in the role of geographic information systems in various fields of human activity. However, solving complex problems requires the use [...] Read more.
The rapid growth of geographic information technologies in the field of processing and analysis of spatial data has led to a significant increase in the role of geographic information systems in various fields of human activity. However, solving complex problems requires the use of large amounts of spatial data, efficient storage of data on on-board recording media and their transmission via communication channels. This leads to the need to create new effective methods of compression and data transmission of remote sensing of the Earth. The possibility of using fractal functions for image processing, which were transmitted via the satellite radio channel of a spacecraft, is considered. The information obtained by such a system is presented in the form of aerospace images that need to be processed and analyzed in order to obtain information about the objects that are displayed. An algorithm for constructing image encoding–decoding using a class of continuous functions that depend on a finite set of parameters and have fractal properties is investigated. The mathematical model used in fractal image compression is called a system of iterative functions. The encoding process is time consuming because it performs a large number of transformations and mathematical calculations. However, due to this, a high degree of image compression is achieved. This class of functions has an interesting property—knowing the initial sets of numbers, we can easily calculate the value of the function, but when the values of the function are known, it is very difficult to return the initial set of values, because there are a huge number of such combinations. Therefore, in order to de-encode the image, it is necessary to know fractal codes that will help to restore the raster image. Full article
(This article belongs to the Special Issue Fractal Geometry in Geospatial Data Analysis)
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