The convergence of the periodic system indicates historical patterns in the structure of the system, especially in the similarity among chemical elements. By using methods of time series analysis, the evolution of the periodic system can be further explored by retrieving details on the trends of particular similarities and their variability according to the the expansion of the chemical space. Time series analysis approaches may therefore shed light on the memory processes along the evolution of the periodic system, which contributes to the understanding of the convergence of the periodic system as triggered by the path-dependent evolution of the chemical space. In this respect, it is important to analyse the rise of the periodic system as an organisational principle in chemistry, which may have contributed to the expansion of the space in a self-reinforced manner. That is, to what extent the periodic system has contributed to explore certain kind of chemistry instead of another as motivated by trying to reproduce or challenge the patterns of the periodic system? How far is the evolution of the periodic system from a self fulfilling prophecy? -to use Merton's expression . We found initial evidence of these processes, for instance with the exploration of Si and Ge chemistries by trying to reproduce the chemistry of the members of their group on the periodic system. Similar approaches are followed when exploring the chemical possibilities of super heavy elements .