Recent Advances in the Applications of Fractal Dimension in Urban Studies

Dear Colleagues,

Fractal geometry is an effective tool for exploring complex systems such as cities, and the fractal dimension is a characteristic parameter for describing scale-free phenomena, including urban form, growth, and structure; self-organized networks of cities; city size distribution; and allometric growth. Urban geographical phenomena fall into two categories: those with and those without characteristic scales (scale-free phenomena). The former can be described with conventional measurements and mathematical methods, while the latter should be characterized by scaling exponents such as fractal parameters. Conventional mathematical modeling and quantitative analysis are based on a characteristic scale, termed characteristic length in the literature. However, complex systems bear no characteristic length in many aspects and cannot be effectively modeled or analyzed by conventional mathematical methods. One of the proper approaches to exploring complex systems is scaling analysis, and fractal geometry is a powerful tool for this. Fractal dimension can be used to characterize complex spatial and hierarchical structures. Based on fractal parameters, effective mathematical models can be constructed for the scale-free distribution of cities. Moreover, fractals represent the optimized structure in nature and society; a fractal body can occupy its space in the most effective way. By means of ideas from fractals and fractal dimension, we may be able to develop new theories and methods for the organization of urban structure.

The focus of this Special Issue relates to the exploration of applications of fractal dimension in the theory, practice, and methodology of urban science. Topics that are invited for submission include (but are not limited to) the following:

• Fractal dimension for the scaling analysis, allometric growth, rank size distribution, system analysis, and structural optimization of cities;
• Fractal dimension based on the spectral analysis and correlation function analysis of cities;
• Mathematical modeling and the development of quantitative analysis methods based on fractal parameters of cities;
• Self-affine fractals for the time-series analysis of cities;
• Laplacian fractals for modeling self-organized networks of cities;
• Multifractal scaling for the charactization of cities;
• Statistical analysis based on fractal dimension of cities.

Prof. Dr. Yanguang Chen
Guest Editor

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.

• fractals
• fractal dimension
• fractal cities
• spatial complexity
• urban studies