Foundations and Clinical Applications of Fractal Dimension in Neuroscience: Concepts and Perspectives

Fractal geometry offers a mathematical framework to quantify the complexity of brain structure and function. The fractal dimension (FD) captures self-similarity and irregularity across spatial and temporal scales, surpassing the limits of traditional Euclidean metrics. In neuroscience, FD serves as a key descriptor of the brain’s hierarchical organization—from dendritic arborization and cortical folding to neural dynamics measured by diverse neuroimaging techniques. This review summarizes theoretical foundations and methodological advances in FD estimation, including the box-counting approach for imaging, and Higuchi’s and Katz’s algorithms for electrophysiological data, addressing reliability and reproducibility issues. In addition, we illustrate how fractal analysis characterizes brain complexity in health and disease. Clinical applications include detecting white matter alterations in multiple sclerosis, atypical maturation in intrauterine growth restriction, reduced cortical complexity in Alzheimer’s disease, and altered neuroimaging patterns in schizophrenia. Emerging evidence highlights FD’s potential for distinguishing consciousness states and quantifying neural integration and differentiation. Bridging mathematics, physics, and neuroscience, fractal analysis provides a quantitative lens on the brain’s multiscale organization and pathological deviations. FD thus stands as both a theoretical descriptor and a translational biomarker whose standardization could advance precision diagnostics and understanding of neural dynamics.