• {Mg, Ca, Sr, Hg} , {Li, Na, K} SI Fig. : Reshuffling of similarity matrix of year 2021 as ordered by atomic number Z and three optimised sequences. Elements arranged by (left) atomic number and (rest of the row) by optimised sequences of elements (Methods 6.3). As can be seen, the search for optimal element sequences groups together highly similar elements into blocks with high contrast relative to the background. This result motivates the use of computer vision algorithms (Methods 6.7) for detecting families of elements. It is also illustrated how different optimisations, for the same similarity matrix, often produce in different images, nevertheless with similar local structures, that is, roughly the same blocks are found, although in different positions within the matrix. The complete set of matrices and results of the optimisations is provided in the . SI Fig. : Similarity between element sequences correlates well with difference in cost L. Correlation between difference in L, and similarity between element sequences (Methods 6.4). Each column corresponds to a different value of r. A bag of sequences was built from all element sequences obtained from the optimisations 6.3, for a total of 11,000. Top row compares the best obtained sequence overall, against all others. Bottom row compares a randomly chosen sequence, against all others. Each column corresponds to a different value of r. The parameter r used in the computation of similarity between sequences of elements (Methods 6.4) corresponds to a radius that defines a neighbourhood around each element in the sequence. The higher the values of r, the more loose the comparison becomes as the neighbourhoods become larger. In the limit when r approaches half of the number of elements in a sequence, all possible sequences are equal under this quantity. Thus low values of r are desired, to evaluate how local structures (in small neighbourhoods of each element) are preserved from one sequence to the other. The plot shows that r=2 is already a good choice, for which r = 2 is used for the computations in this work.