Fractal Dimensions with Applications in the Real World
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Geometry".
Deadline for manuscript submissions: 31 July 2025 | Viewed by 5794
Special Issue Editors
Interests: fractal geometry; topology on fractals; Lipschitz equivalence; Gromov hyperbolic graphs
Interests: computer vision; image processing; machine/deep learning; scientific computing
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
The concept of fractals was introduced by B. Mandelbrot in the last 1970s as a class of highly irregular sets often presenting with infinite complexity, self-similarity and the nonintegral Hausdorff dimension. It has had a great impact in the development of mathematics and many other disciplines of science. In mathematics, fractal originates in chaos and dynamic systems, and soon after it was found that fractals appear in almost every area and are susceptible to systematic studies using classical and contemporary methods. In the last four decades, a large part of fractal research has been related to the dimension theories and structures of self-similar sets and measures.
The aim of this Special Issue is to present the up-to-date progress in fractal dimensions and their various applications to the real world. Topics invited for submission include, but are not limited to, the following:
- Fractal dimensions of iterated function systems;
- Fractal dimensions of self-similar measures;
- Hausdorff dimension of fractal graphs;
- Lipschitz equivalence of fractal sets;
- Topological structures of fractal sets;
- Diophantine approximation;
- Fractal dimensions in dynamical systems;
- Applications of fractal dimensions.
Dr. Jun Luo
Dr. Xiaohao Cai
Dr. Liang-Yi Huang
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
- iterated function systems
- self-similar sets
- self-affine sets
- fractal measures
- fractal graphs
- beta-expansions
- Hausdorff dimension
- box-counting dimension
- Lipschitz equivalence
- topological structures
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