The Backbone of Fractals: Feedback and the Iterator

Abstract

Unfortunately, May’s emphatic message has remained largely unheard, at least as far as mathematics education is concerned. What are the phenomena to which he refers? And why is he convinced that they are of such outstanding importance? We will carefully imbed his message into a larger frame before we explore his results in greater detail.

I would therefore urge that people be introduced to the logistic equation early in their mathematical education. This equation can be studied phenomenologically by iterating it on a calculator, or even by hand. Its study does not involve as much conceptual sophistication as does elementary calculus. Such study would greatly enrich the student’s intuition about nonlinear systems. Not only in research but also in the everyday world of politics and economics, we would all be better off if more people realized that simple nonlinear systems do not necessarily possess simple dynamical properties.

Robert M. May¹