Fractal Dynamics of Complex Systems in Society and Behavioral Science

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

Deadline for manuscript submissions: 20 May 2026 | Viewed by 504

Special Issue Editors


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Guest Editor
Department of Chemical and Biomolecular Engineering, John Hopkins University, Baltimore, MD 21218, USA
Interests: fractals; biophysics; geometric transformation; navier stokes equations; mathematical physics; vector calculus

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Guest Editor
School of Science, Beijing Jiaotong University, No 3. Shangyuancun, Haidian District, Beijing 100044, China
Interests: differential equations; bifurcation and chaos of nonlinear dynamical system; complex networks; numerical methods
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Special Issue Information

Dear Colleagues,

Fractal patterns emerge ubiquitously in nature—arising from purely physical dynamics, such as lightning strikes, as well as from biologically driven collective behaviors, such as those observed in bacterial colonies. In this Special Issue, we focus on the latter – exploring how fractal collective dynamics emerge across scales, from physical systems of interacting particles and swarms to complex societal and intelligent communities. We aim to showcase the richness and depth of insights from physics, biology, cognitive science, and social theory that shed light on how local interactions among agents give rise to fractal (scale-free and/or fractional) global structures and emergent organization.

We welcome theoretical, computational, and experimental/empirical studies that reveal fractalities in behavior, communication, organization, and decision-making. We especially encourage interdisciplinary work linking microscopic rules to macroscopic phenomena in living, synthetic, and hybrid systems.

Dr. Trung V. Phan
Prof. Dr. Mingshu Peng
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 dynamics
  • scale free
  • collective behavior
  • self-organization
  • adaptive and intelligent systems

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Published Papers (1 paper)

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Review

18 pages, 1540 KB  
Review
From Fractal Geometry to Fractal Cognition: Experimental Tools and Future Directions for Studying Recursive Hierarchical Embedding
by Mauricio J. D. Martins
Fractal Fract. 2025, 9(10), 654; https://doi.org/10.3390/fractalfract9100654 - 10 Oct 2025
Viewed by 350
Abstract
The study of fractals has a long history in mathematics and signal analysis, providing formal tools to describe self-similar structures and scale-invariant phenomena. In recent years, cognitive science has developed a set of powerful theoretical and experimental tools capable of probing the representations [...] Read more.
The study of fractals has a long history in mathematics and signal analysis, providing formal tools to describe self-similar structures and scale-invariant phenomena. In recent years, cognitive science has developed a set of powerful theoretical and experimental tools capable of probing the representations that enable humans to extend hierarchical structures beyond given input and to generate fractal-like patterns across multiple domains, including language, music, vision, and action. These paradigms target recursive hierarchical embedding (RHE), a generative capacity that supports the production and recognition of self-similar structures at multiple scales. This article reviews the theoretical framework of RHE, surveys empirical methods for measuring it across behavioral and neural domains, and highlights their potential for cross-domain comparisons and developmental research. It also examines applications in linguistic, musical, visual, and motor domains, summarizing key findings and their theoretical implications. Despite these advances, the computational and biological mechanisms underlying RHE remain poorly understood. Addressing this gap will require linking cognitive models with algorithmic architectures and leveraging the large-scale behavioral and neuroimaging datasets generated by these paradigms for fractal analyses. Integrating theory, empirical tools, and computational modelling offers a roadmap for uncovering the mechanisms that give rise to recursive generativity in the human mind. Full article
(This article belongs to the Special Issue Fractal Dynamics of Complex Systems in Society and Behavioral Science)
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