Fractals in the neurosciences, part I: General principles and basic neurosciences

Antonio Di Ieva*, Fabio Grizzi, Herbert Jelinek, Andras J. Pellionisz, Gabriele Angelo Losa

*Corresponding author for this work

    Research output: Contribution to journalReview articlepeer-review

    130 Citations (Scopus)


    The natural complexity of the brain, its hierarchical structure, and the sophisticated topological architecture of the neurons organized in micronetworks and macronetworks are all factors contributing to the limits of the application of Euclidean geometry and linear dynamics to the neurosciences. The introduction of fractal geometry for the quantitative analysis and description of the geometric complexity of natural systems has been a major paradigm shift in the last decades. Nowadays, modern neurosciences admit the prevalence of fractal properties such as self-similarity in the brain at various levels of observation, from the microscale to the macroscale, in molecular, anatomic, functional, and pathological perspectives. Fractal geometry is a mathematical model that offers a universal language for the quantitative description of neurons and glial cells as well as the brain as a whole, with its complex three-dimensional structure, in all its physiopathological spectrums. For a holistic view of fractal geometry of the brain, we review here the basic concepts of fractal analysis and its main applications to the basic neurosciences.

    Original languageEnglish
    Pages (from-to)403-417
    Number of pages15
    Issue number4
    Publication statusPublished - Aug 2014


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