Double pendulum
Two rods hinged end to end, or three, swinging under gravity with nothing random in them. Drag a bob and let it go, or run a few hundred that start a whisker apart and watch how quickly they part company.
Trace and fan
The tip of the last arm draws where it has been. Trail length is how long a mark takes to fade to half. Keep the whole drawing switches the fading off, so an hour of swinging piles up into one picture, and Save image writes it out at twice the size you see.
Chaos fan runs many copies at once, coloured from red to violet, whose starting angles differ by no more than the spread. They begin as one line. The panel in the corner plots how far apart their tips are, on a scale where each gridline is ten times the last, so a straight climb is the spread multiplying at a steady rate. Automatic measures the machine and picks a count it can hold at full speed.