Lorenz Attractor

The Lorenz system is a set of equations that specifies rules for how the position of a point in 3D space changes with time. This image is one of the trajectories that follow these equations. In particular, the Lorenz equations are used to model the trajectory of fluid particles in a layer of liquid that was heated from below and cooled from above. 

The trajectories follow two lobes that resemble butterfly wings. The system is considered "chaotic". In maths, this means that if we chose a slightly different starting point, the path taken orbiting these lobes would be very different. Notice that sometimes the path circles one lobe multiple times before switching to the other lobe, and other times it only does one loop. If we varied our initial starting point a tiny bit and generated the trajectory again, the new path around the lobes would vary in a way that we could not predict from our knowledge of this original path. 

This image is often linked to the concept of the "butterfly effect" to describe how small changes in a complex system (like global weather systems) can have significant and difficult-to-predict effects.