Quaternion Animal Kingdom by Doug Sweetser

Wolves eat Rabbits. Alligators eat Frogs and Turtles. 
Quaternions, time + 3D, power all the motion in this Kingdom.
 
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The wolves hunt in a pack, targeting one rabbit at a time. The rabbit females try to avoid the wolves, using an inverse square weighting to avoid all wolves on the screen. The male rabbits use the same inverse square to chase fertile females. 
The frogs hop and hang out in the shallow end of the lake. 
All numbers used to describe this world are quaternions, including:  
  • position
  • change in position
  • change in change in position
The hunting behavior of wolves is controlled with with change in change in position, which formally is not acceleration.  Similar things happen in control theory (but never using quaternions :-)
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