Statistical properties of an iterated arithmetic mapping

We study the (3x+1)/2 problem from a probabilistic viewpoint and show a forgetting mechanism for the lastk binary digits of the seed afterk iterations. The problem is subsequently generalized to a trifurcation process, the (lx+m)/3 problem. Finally the sequence of a set of seeds is empirically shown to be equivalent to a random walk of the variable log2x (or log3x) though computer simulations.