FRACTAL ASPECTS OF NATURAL GROWTH

The work presented here puts forward a fractal aspect of natural growth. The S-shaped pattern of a logistic function is analyzed in terms of several constituent logistic functions. The approach sheds light on two familiar phenomena: the undulatory evolution of growth, which gives rise to an alternation between high- and low-growth periods, and the increasingly noticeable shrinking life cycle of products. There are some economic and political implications for the European nations. A quantitative example is given for computer sales from Digital Equipment Corporation. The approach is further generalized to suggest that any growth process can be analyzed in terms of natural-growth subprocesses. Applied to human growth this analysis yields precise definitions for the timing of transitions such as babyhood to childhood, and childhood to adolescence.