Fractal Scaling within an Organism

Nat ralists observe, a Flea Hath smaller Fleas that on him prey And these have smaller Fleas to bite em. 

FIGURE 7.4.1 This is an example of a self-similar geometry. Patterns apparent at larger scales are repeated as smaller scales. A pattern such as is illustrated here is typical of the respiratory system and of many plants. 

Self-similar structures do not have a single length scale. The property of interest (say the diameters of the respiratory airways, for instance) will then be dependent on the scale of interest, usually decreasing in value as the scale becomes smaller (West and Goldberger, 1987). The result is that instead of an exponential function where the ratio of larger scale to smaller scale is a constant, the larger scale is related to the smaller scale through a power law relationship. 

Fractals can also be inferred from morphogenesis (the development of form or structure), where a single time scale does not adequately address all time-dependent processes. The electrocardiogram seems to have fractal time properties, as well as electrical activity of a single neuron and beat-to-beat variability of the heart rate. There are also fractal (power law) variations in blood neutrophil counts. Further research will probably turn up other cases of self-similarity. 

---