The functions shown on these plots are surprisingly similar to one another. The terms for each plot consist of sine and cosine. The amplitude depends on phase, and a phase offset depends on amplitude. The primary distinction between the collection of periodic and chaotic orbits is the use of 2pi vs. 10 as a denominator. Using 10 resulted in an irrational number. Because the relationship between the horizontal and vertical components is very nonlinear, we see distinctions between the original and irrational functions within several iterations. 

In a collisionless space plasma (also known as outer space), we see nonlinear waves upstream of shock waves. The nonlinearity arises from the two-way interaction between shock-reflected charged particles and electromagnetic fields. The reflected particles generate electromagnetic waves, and the waves alter the energy distributions of the particles.

The light green curve with open ends is closed in the sense that the path is retraced many times. You can imagine this curve as a pendulum trace.

The image second from the right side is a long-exposure LED poi trace in the vertical (wall) plane. The other images are plots were created using mathematical functions.