Proceeding of International Conference
Toshiyuki Kumano, Tetsushi Ueta, Hiroshi Kawakami, Pattern Emergence in Strange Attractor by Directions of Mappings, Proc. of ISCAS2006, 2737-2740, Island of Kos, Greece, May 2006.
Abstract: This paper proposes a new visualization method to given chaotic attractors in discrete nonlinear dynamical systems. Conventionally it is expressed by plotting the solution orbit into a plane as a set of dots. In the case of color figures, a pixel is colored by the location of the orbit, histogram of hitting, and so on. We use an argument defined by a current orbit and an n-time mapped point is utilized for coloring. This can depict orientation or tendency of the orbit within the chaotic attractor. In this visualization process, an remarkable pattern emergence phenomenon is observed. We illustrate these color figures and discuss similarity to basins of attraction.