Let α = {Ca, Ba, Na, K, Li, H, Cl, Br, I, F}, and α ={Li, H, Na, Ba, K, Ca}; note that they have different amount of elements (10 and 6, respectively), which illustrates how sequences with different sizes can be compared. SI Fig. : Similarity matrices between elements over the years. Selected examples of similarity matrices, with rows and columns sorted according to atomic number. The obtained similarity matrices are highly structured objects containing blocks around the main diagonal, as well as diagonal and vertical/horizontal patterns. The former correspond to similarities among neighbouring elements belonging in the same period of the periodic table. For instance C, N, O and F; or Mn, Fe, Co, Ni, Cu and Zn; and the lanthanoids (from La to Lu). Diagonal patterns show similarities among elements belonging in the same family, traditionally depicted as elements of a column (group) on the conventional periodic table. Exceptions to the over-simplistic group-period characterisation of the periodic system are shown, for instance the similarity between Mg and Zn, which belong to current group 2 and 12, respectively. The closest diagonal patterns to the main diagonal correspond to neighbouring elements belonging to adjacent periods on the periodic system, from 3 rd to 6 th ; that is, there are similarities among 3 rd and 4 th period elements, 4 th and 5 th , etc. Similarities among 2 nd and 3 rd period elements are much lower, which evidences the validity of the singularity principle of second period elements . A second diagonal pattern is observed farther from the main diagonal and corresponds to similarities between 3 rd and 5 th periods (secondary periodicity ). This is the case of the similarities between Mg-Cd and Al-In, for instance. Horizontal/vertical patterns are caused by the resemblance of lanthanoids regarding other elements. This is the case of their similarities with Y and Sc, which constitute the rare earths together with the lanthanoids (La-Lu). They also show some similarities with Al, Ga and In (yellow horizontal lines on top of the block), which share the typical +3 valency of lanthanoids.