  We consider a mechanical system of three ants on the floor, which move
according to two independt rules: Rule A - forces the velocity of any given ant
to always point at a neighboring ant, and Rule B - forces the velocity of every
ant to be parallel to the line defined by the two other ants. We observe that
Rule A equips the 6-dimensional configuration space of the ants with a
structure of a homogeneous (3,6) distribution, and that Rule B foliates this
6-dimensional configuration space onto 5-dimensional leaves, each of which is
equiped with a homogeneous (2,3,5) distribution. The symmetry properties and
Bryant-Cartan local invariants of these distributions are determined.
  In the case of Rule B we study and determine the singular trajectories
(abnormal extremals) of the corresponding distributions. We show that these
satisfy an interesting system of two ODEs of Fuchsian type.
