The periodic system encodes order and similarity among chemical elements arising from known substances at a given time that constitute the chemical space. Although the system has incorporated new elements, the connection with the remaining space is still to be analysed, which leads to the question of how the exponentially growing space has affected the periodic system. Here we show, by analysing the space between 1800 and 2021, that the system has converged towards its current stable structure through six stages, respectively characterised by the finding of elements (1800–1826), the emergence of the core structure of the system (1826–1860), its organic chemistry bias (1860–1900) and its further stabilisation (1900–1948), World War 2 new chemistry (1948–1980) and the system final stabilisation (1980–). Given the self-reinforced low diversity of the space and the limited chemical possibilities of the elements to be synthesised, we hypothesise that the periodic system will remain largely untouched.