Simulation analysis of statistical properties of random polygonal lines iteratively generate on the plane

Using renormalization, we compute a scale factor such that the distance of the endpoints of a Pacheco d´Amorim random polygonal line in the plane is a non-degenerate random variable. We also analyze more general random polygonal lines and the corresponding limit curves, folded at random points of the segments at each iterative step of its construction, instead of the middle point.