In each triplet of ladybugs the bugs are chasing each other. There are six such triplets. Press Space to start the chase. Press 'a' to get new initial positions (evenly spread). The bugs can be moved around before starting the chase, to get different patterns. Edit: Added a change in shade thanks to a suggestion from dapontes.
Each triplet works like Pursuit curve 1 (http://scratch.mit.edu/projects/11253495/ ). This is an explanation for how one such triplet is drawn: In each step, each Ladybug moves 'step' towards the next Ladybug. The traces of the ladybugs are spiral-shaped. These spirals are the actual curves of pursuit. The pattern formed also contains the polygons that in each step is drawn between the ladybugs. In order to draw the polygons, in each step a clone moves to the next Ladybug. Wikipedia - Pursuit curve: http://en.wikipedia.org/wiki/Pursuit_curve