Persecution Complexified

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

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

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:

square+midpoint+2


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

square+midpoint+3


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:

square+various_displacements


square+varioussquare+midpoint+2


square+midpoint+3


square+4sidepoints+various


square+4sidepoints+4


square+3sidepoints+6


square+3sidepoints+5


square+2sidepoints+5


square+2sidepoints+4


triangle+various

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