Chaotic pendulum

The movement of the magnetic pendulum depends on many factors, like the friction (it can be enhanced if the pendulum is submerged in a liquid), the gravity force (which changes the relative direction if the vertical positioning of the pendulum changes), the attracting or repelling force of magnets (different magnets have slightly different strengths and configurations so they never act with exactly the same force).

Let us paint single "gates" with different colours and check in many runs where the pendulum stops, if launched from "exactly" the same position. Then change the initial position and start again. You will get a nice picture.

The picture here is the "flag" picture of the research into chaos. It is called Lorenz's attractor or butterfly effect, as it resembles a real butterfly. The line never returns to its previous track and trajectories are separate.

Both pictures belong to the class called "fractals", as they are composed of smaller fractions resembling the whole picture. An example of fractals is the common cauliflower, as it is composed of smaller flowers, being copies of the whole one.