It can be seen as the pattern created by five dogs chasing each other’s tails and moving a small fixed distance at each moment. Now imagine five kangaroos chasing each other’s tails and moving half the remaining distance-to-tail at a single bound:
Other patterns appear when the kangaroos bound towards a fixed point, which changes at each bound. Here each kangaroo bounds towards a point two places ahead of the point towards which it last bounded:
Standard pursuit curves can become more complicated when points are added between the points of the standard polygon, as is seen in this animated gif:
Non-standard pursuit curves can be complicated too. Here is one in which the bound distance varies from 0% to 100% in 5% increments:
Here the image quadruples in size in each frame of the animated gif:
Other variables of the chase algorithm can be adjusted to produce other effects. The following two shapes differ in whether each chasing animals moves towards the first position of the tail it began chasing or towards the tail’s current position (a different tail or tail’s-original-position is chased at each move). In this pattern, the original position is chased:
In this pattern, the tail’s current position is chased (and the pattern, like the one directly above, doubles in size in each frame):
