The self-drawing pendulum

On the left, a pendulum swings and slowly gives up its energy to friction. On the right it plots its own state — angle across, speed up — and the plot spirals inward toward the single point where it comes to rest.

The maths: the state is the pair (angle, angular speed). The rule θ″ = −(g/L) sin θ − c θ′ turns that pair into the next one. Read The pendulum that draws itself.