This chapter is dedicated to the memory of Professor Jean Paul Rigaut, who passed away in 2005, and who pioneered the adoption of fractal geometry in the biomedical sciences.
Fractals in Biology and Medicine
Published Online: 10 OCT 2011
Copyright © 2006 Wiley-VCH Verlag GmbH & Co. KGaA. All rights reserved.
Reviews in Cell Biology and Molecular Medicine
How to Cite
Losa, G. A. 2011. Fractals in Biology and Medicine. Reviews in Cell Biology and Molecular Medicine. .
- Published Online: 10 OCT 2011
The extension of the concepts of fractal geometry towards the life sciences has led to significant progress in understanding the complex functional properties and architectural/morphological/structural features that characterize cells and tissues during ontogenesis and also in both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms. Fractals fulfill a certain number of theoretical and methodological criteria, including a high level of organization, shape irregularity, functional, and morphological self-similarity, scale invariance, iterative pathways, and a peculiar noninteger fractal dimension (FD). Whereas, mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits – termed the scaling window – in which the relationship between the scale of observation and the measured size or length of the object can be established. For statistically self-similar irregular objects, the size and geometric parameters differ when inspected at increasing resolution, which reveals more details. Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also show why the application of the fractal principle is valuable for measuring the dimensional, geometrical, and functional parameters of cells, tissues, and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a “Fractal Geometry of Life” may be envisaged, and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of fractalomics.
- Fractal (fractional) dimension;
- Form invariance;
- Scaling window;