The use of image processing techniques in rendering maps with deterministic chaos

Abstract

Chaos theory 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. In this paper, bifurcation maps of the equation Xt+1=λXt[1+Xt]-β 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. © 1988 Springer-Verlag.