Fractals in biology and medicine

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This compilation features presentations from the Fourth International Symposium on Fractals in Biology and Medicine, held in Ascona, Switzerland, on March 13, 2004, in honor of Professor Benoît Mandelbrot's 80th birthday. The symposium, part of a series that began in 1993, includes 29 contributions organized into four sections: Fractal structures in biological systems, neurosciences, tumours and diseases, and the fractal paradigm. Mandelbrot's concepts—scale invariance, self-similarity, irregularity, and iterative processes—have inspired significant advancements in biomedical sciences. These ideas facilitate a deeper understanding and analytical description of complex hierarchical scaling processes, chaotic systems, non-linear dynamics, and transport diffusion events across membrane surfaces. They also apply to morphological structures and biological shapes in both healthy and diseased states. While many biological processes can be modeled using power law behavior characterized by a single parameter (the fractal dimension D), alternative models have been developed to describe fractional time dynamics and space behavior. These fractional mechanisms enable the integration of spatial and functional effects through two fractional parameters, addressing diverse aspects discussed by biomedical subjects at the symposium.