Pattern emergence in strange attractors by directions of mappings

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, a remarkable pattern emergence phenomenon is observed. We illustrate these color figures and discuss similarity to basins of attraction