Imagine four mice sitting on the corners of a square. Each mouse begins to run towards its clockwise neighbour. What happens? This:

Four mice chasing each other

The mice spiral to the centre and meet, creating what are called pursuit curves. Now imagine eight mice on a square, four sitting on the corners, four sitting on the midpoints of the sides. Each mouse begins to run towards its clockwise neighbour. Now what happens? This:

Eight mice chasing each other

But what happens if each of the eight mice begins to run towards its neighbour-but-one? Or its neighbour-but-two? And so on. The curves begin to get more complex:

(Please open the following image in a new window if it fails to animate.)

You can also make the mice run at different speeds or towards neighbours displaced by different amounts. As these variables change, so do the patterns traced by the mice:

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