A NOTE ON CHAOS AND HALLEY’S METHOD

This note illustrates very simple graphics techniques for visualizing a large class of graphically interesting manifestations of chaotic behavior arising from com-plex analytic dynamics. Another goal of this note is to give a flavor of the subject of recurrence relations and chaos. As background, research over the past decade has made it clear that many systems of physical, biolog-ical, electrical, and chemical interest exhibit highly un-stable or chaotic behavior [2-51, [14]. Chaos theory often involves the study of how complicated behavior can arise in systems which are based on simple rules, and how minute changes in the input of a system can lead to large differences in the output. Chaotic behavior in such systems is generally irregular and disorderly-examples include weather patterns, some neurologica