The fractal geometry of life.

The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and 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 (Weibel [1991]). Fractals fulfil 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 non-integer 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, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring 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".