Graphics, Bifurcation, Order and Chaos

Abstract

Chaos theory involves the study of how complicated behaviour 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. In this paper, bifurcation maps of the education Xt+1=??Xt [1+Xt] -?, where ?= 1 or ?=e-Xi, are presented, and they reveal a visually striking and intricate class of patterns ranging from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. The computer-based system presented is special in its primary focus on the fast characterization of simple"chacs equation" data using an interactive graphics system with a variety of controlling parameters.