Applications of Fractal Geometry in Surface 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: 31 March 2027 | Viewed by 600

Editors


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Laboratório de Desenvolvimento e Aplicações de Nanomateriais da Amazônia (LADENA), Materials Physics Department, Federal University of Amazonas-UFAM, Manaus 69067-005, AM, Brazil
Interests: AFM; SEM; TEM; surfaces; topographical and morphological characterization of three-dimensional surfaces at the micro/nanoscale; development of new mathematical tools in the investigation of 3D surface quality; theoretic and applied research in advanced materials science in applied sciences; mechanical and tribological characterization of macro–micro-nanostructures; experimental techniques for micro/nanomechanical and micro/nanotribological characterization; fractal and multifractal geometry analysis and applications
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Centro Multiusuário para Análise de Fenômenos Biomédicos. Universidade do Estado do Amazonas, Manaus 69065-001, AM, Brazil
Interests: biological surfaces; microbiology and parasitology

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Amazonian Materials Group, Department of Physics, Federal University of Amapá, Macapá 68903-419, Brazil
Interests: photocatalysis; nanostructured catalysts; environmental catalysis; biomass-derived nanomaterials; magnetic nanocomposites; green synthesis; surface characterization; atomic force microscopy (AFM); semiconductor materials; thin films
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractal geometry has emerged as a valuable framework for understanding the complexity of natural forms, especially in biological systems where surface structures often defy traditional geometric description. This Special Issue of Fractal and Fractional aims to explore the growing role of fractal and multifractal analysis in surface science, with a particular focus on applications in life sciences and biophysics. We welcome contributions that investigate biological surfaces—such as tissues, cell membranes, biofilms, and biomaterials—through the lens of fractal geometry. These surfaces frequently exhibit irregularities and patterns across multiple length scales, making them ideal candidates for fractal-based quantitative analysis. Studies applying techniques such as atomic force microscopy (AFM), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and optical profilometry, combined with surface descriptors like roughness parameters, fractal dimension, lacunarity, multifractal spectra, and Minkowski functionals, are especially encouraged for submission. This Special Issue seeks to promote interdisciplinary dialogue between physicists, biologists, engineers, and material scientists working at the interface between structure and function. We are particularly interested in work that demonstrates how fractal-based metrics can enhance our understanding of biological function, pathological processes, biomaterial performance, or the development of new diagnostic and analytical tools. Experimental, theoretical, and computational approaches—especially those combining high-resolution imaging with advanced data analysis—are all welcome.

Dr. Henrique Duarte da Fonseca Filho
Dr. Glenda Quaresma Ramos
Dr. Robert S. Matos
Guest Editors

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Keywords

  • fractal geometry
  • multifractals
  • surface roughness
  • biophysics
  • AFM/SEM/TEM in life sciences
  • morphological complexity
  • biomaterials
  • surface characterization
  • lacunarity
  • minkowski functionals

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Published Papers (1 paper)

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Research

20 pages, 27457 KB  
Article
Topological–Multifractal Characterization of Adaxial–Abaxial Leaf Surface Asymmetry in Theobroma grandiflorum via Minkowski Functionals and Confocal Profilometry
by Ricardo Cruz de Souza, Filho, Adriana de Souza Fontes, Emanuel Félix Andrade Ramos, Glenda Quaresma Ramos, Robert Saraiva Matos, Mariane Peres Pereira, Carlos Alberto Rodrigues Costa and Henrique Duarte da Fonseca, Filho
Fractal Fract. 2026, 10(8), 535; https://doi.org/10.3390/fractalfract10080535 - 5 Aug 2026
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Abstract
This study presents a unified topological and multifractal framework for the characterization of leaf surface complexity in Theobroma grandiflorum. By combining laser scanning confocal microscopy (LSCM)-derived three-dimensional profilometry with Minkowski functionals and multifractal analysis, we quantitatively distinguished the structural organization of adaxial and [...] Read more.
This study presents a unified topological and multifractal framework for the characterization of leaf surface complexity in Theobroma grandiflorum. By combining laser scanning confocal microscopy (LSCM)-derived three-dimensional profilometry with Minkowski functionals and multifractal analysis, we quantitatively distinguished the structural organization of adaxial and abaxial surfaces beyond conventional morphological descriptions. The analysis of the Minkowski functionals revealed distinct connectivity regimes and threshold-dependent transitions, indicating differences in surface topology and percolation behavior. These findings were further supported by multifractal spectra, which exhibited a broader distribution of singularities for the abaxial surface, reflecting increased heterogeneity and structural complexity. The introduction of the normalized differential parameter ΔP proved to be an effective strategy for directly quantifying morphological asymmetry, while radar plots enabled an integrated visualization of multivariate descriptors. From a physical perspective, the observed differences are consistent with the functional specialization of leaf surfaces, where the abaxial side exhibits greater structural complexity associated with gas exchange and environmental interaction, while the adaxial surface remains more compact and protective. Overall, the proposed approach advances the application of fractal and topological methods to biological systems, offering a scalable and transferable framework for the analysis of complex natural surfaces. This methodology opens new perspectives for studies in plant morphology, taxonomy, and environmental adaptation, aligning with the broader scope of fractal and fractional analysis in complex systems. Full article
(This article belongs to the Special Issue Applications of Fractal Geometry in Surface Science)
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