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Fractal Theory: A Comprehensive Review Of Applications Across Engineering Disciplines

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  • ROBERT FRISCHER

    (Research Center, Skoda Auto University, Na Karmeli 1457, 293 01 Mlada Boleslav, Czech Republic)

  • MAYUR PRATAP SINGH

    (Department of Mechanical Engineering, School of Engineering, Galgotias University, Greater Noida, Uttar Pradesh 203201, India)

  • CAMILLO PORCARO

    (Department of Neuroscience and Padova Neuroscience Center, University of Padova, Padova, Italy4Institute of Cognitive Sciences and Technologies-National, Research Council, Rome, Italy5Centre for Human Brain Health and School of Psychology, University of Birmingham, Birmingham, UK)

  • HAMIDREZA NAMAZI

    (Research Center, Skoda Auto University, Na Karmeli 1457, 293 01 Mlada Boleslav, Czech Republic6Biomedical Signal & Image Processing Lab, Galgotias University, Greater Noida, Uttar Pradesh 203201, India7School of Engineering, Monash University, 47500 Subang Jaya, Selangor, Malaysia)

Abstract

Fractal theory has gained increasing attention across various engineering disciplines due to its ability to model complex, self-similar, and multiscale phenomena. This paper presents a comprehensive review of fractal applications in biomedical, mechanical, civil, environmental, and materials engineering. In particular, fractal analysis has enabled optimizing porous scaffolds in biomaterials to improve tissue integration and mechanical performance. In biomedical signal processing, fractal algorithms have improved the detection and classification of neurological disorders, particularly through electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) complexity measures. Additionally, fractal-based models have been effectively used in environmental engineering to improve the prediction and control of pollution dispersion in heterogeneous landscapes. This paper also outlines key theoretical foundations, computational methods, and domain-specific innovations, while identifying current challenges and future directions. By integrating these advances, this review provides a roadmap for using fractal theory in both theoretical research and practical applications.

Suggested Citation

  • Robert Frischer & Mayur Pratap Singh & Camillo Porcaro & Hamidreza Namazi, 2025. "Fractal Theory: A Comprehensive Review Of Applications Across Engineering Disciplines," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(07), pages 1-18.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:07:n:s0218348x25300089
    DOI: 10.1142/S0218348X25300089
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