The Significance of Fractals for Biology and Medicine An Introduction and Summary

Abstract

In his seminal book The Fractal Geometry of Nature Benoit Mandelbrot made the point that the mathematical construct of a geometry which allows for fractional dimensions will prove most useful in the characterization of natural phenomena, structures and processes alike. This should be particularly true in biology for a number of reasons. First, the complex structure of living creatures, from the whole organism down to the cells, is notoriously difficult to reduce to simple geometric descriptions, and functional processes have very often non-linear properties. Organisms develop and grow from small and simple units to gradually achieve their size and complexity. In living systems, design and performance commonly combine strict rules with some random variation which gives each individual its species characteristics and its individual traits. Furthermore, the wonderful variety observed in the plant and animal kingdoms is the result of stepwise “variation over a common theme” — they are similar but not alike with basic features preserved between related species but expressed in different size and proportions.