In exploration mode, you can choose the number of initial points (bugs), and adjust their positions. You can choose different styles of line generation, and colouring. There are three behaviour options — brave means the bugs move at constant speed, timid means they get slower as they get closer but always move at the same speed as each other, and mixed is like timid, but the bugs move at different speeds.
Press and hold the Spin to rotate the pattern. A long press and on the canvas will zoom, and you can use the Save buttons at the bottom to keep copies of your favourite works of mathematical art.
Points: Lines: Shading: Behaviour:
Curves of pursuit are the curves generated when the motion of one point is constantly directed towards another moving point. This is a very difficult problem to solve in the continuous limit, but constructions like those in this activity allow easy approximation for multiple points and speeds.
Incorporating different ways of determining the speed of the points, plus inventive colouring, wonderfully artistic patterns are readily generated.
The figures produced by this activity can be saved and printed—use the Outline line option with no shading to produce figures that can be printed and coloured as worksheets.
Thanks to Clarissa Grandi at Artful Maths for this idea.