Fractal Analysis and Data-Driven Complex Systems

Dear Colleagues,

Complex systems arising in natural, engineered, and social domains often exhibit multiscale, nonlinear, and self-similar structures that cannot be fully described by traditional analytical tools, and require the use of networks, automata, or agent systems. When describing its behaviour, fractal phenomena usually arise, such as scale invariance, irregularity, and long-range dependence in such systems.

In parallel, the existence of vast data availability, data centers and computational resources have permitted the eclosion of artificial intelligence, which is now considered as a research tool in nearly all science fields. In the present context, data-driven methodologies have enabled the extraction of hidden patterns and governing principles from large-scale and high-dimensional data.

This Special Issue aims to bring together fractal theory, computational methods, and data-driven approaches to advance the modeling, analysis, and understanding of complex systems. The focus is on both theoretical developments and applications, emphasizing how fractal concepts can be integrated with modern data-driven techniques to analyze real-world complex phenomena.

The Special Issue welcomes original research articles and review papers on topics including, but not limited to, the following:

Fractal Theory and Methods

• Fractal geometry and multifractal analysis;
• Fractional calculus and fractal operators;
• Scaling laws and self-similarity in complex systems;
• Fractal measures, dimensions, and entropy-based metrics.

Data-Driven and Computational Approaches

• Machine learning and deep learning for fractal feature extraction;
• Data-driven discovery of scaling laws and fractal structures;
• Sparse modeling and reduced-order modeling of fractal systems;
• Anomalous diffusion.

Complex Systems Applications

• Fractal analysis in physics, materials science, and turbulence;
• Biological and physiological signal analysis (e.g., EEG, ECG, genomics);
• Financial markets and economic complexity;
• Climate, geophysical, and environmental systems;
• Urban systems, networks, and social dynamics.

Networks and Dynamical Systems

• Fractal and multifractal properties of complex networks;
• Data-driven modeling of nonlinear and chaotic dynamics;
• Fractional Brownian motion;
• Time-series analysis using fractal-based methods.

Prof. Dr. J. Alberto Conejero
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 250 words) can be sent to the Editorial Office for assessment.

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.

• fractal geometry
• multifractal analysis
• fractional brownian motion
• time-series analysis
• scaling laws and self-similarity