A simple self-organized structure in the example of a sequential growth dynamics of a Causal Set

A simple algorithm of a sequential growth dynamics of an x-graph is considered. The x-graph is a directed acyclic dyadic graph. This model is a particular case of a causal set approach to quantum gravity. The set of vertices of an x-graph is a particular case of a causal set. The sequential growth of an x-graph is a non-deterministic addition of new vertices one by one. The algorithm to add vertices satisfies the causality principle. The considered particular example of the algorithm is based on some random walk on an x-graph. I proved that there is a nonzero probability to generate a self organized connected repetitive structure. This structure consists of any initial connected finite x-graph and a set of infinite sequences of vertices that are connected by double edges.