  We study the dynamics of a transformation that acts on infinite paths in the
graph associated with Pascal's triangle. For each ergodic invariant measure the
asymptotic law of the return time to cylinders is given by a step function. We
construct a representation of the system by a subshift on a two-symbol alphabet
and then prove that the complexity function of this subshift is asymptotic to a
cubic, the frequencies of occurrence of blocks behave in a regular manner, and
the subshift is topologically weak mixing.
