We study the dynamics of a transformation that acts on infinite pathsin the graph associated with Pascal's triangle. For each ergodicinvariant measure the asymptotic law of the return time to cylindersis given by a step function. We construct a representation of thesystem by a subshift on a two-symbol alphabet and then prove that thecomplexity function of this subshift is asymptotic to a cubic, thefrequencies of occurrence of blocks behave in a regular manner, andthe subshift is topologically weak mixing.
