Between 20 and 40 families were obtained for each year, some of which have non-empty intersections -in contrast to the standard periodic table, regarded as a system of partitions. Recurrent families include {Na, K, Rb, Cs}, {Ca, Sr, Ba}, and {F, Cl, Br, I}. To study their evolution, families are selected, that are consistently found over some period in history. Their development is tracked from 1800 to 2021 by comparing each selected family F against the families found for each year. For each family F, and each year y, three cases were considered: 1) F is found in y, 2) F is contained in another family found in y, and 3) None of these. Heat maps showing the results of such analysis are shown below, and a condense picture is given in Fig. . SI Fig. : Calculation of families of elements from a similarity matrix. The method exploits the rich structure of similarity matrices when reshuffled according to the optimised sequences of elements of Methods 6.3, through the use of a computer vision pipeline algorithm for detecting squares in images (Methods 6.7). These results are then processed using a Statistical Noise Reduction algorithm (SNR, Methods 6.8), that outputs the most representative families of elements, given the results from multiple runs of the computer vision pipeline. In the first step, the similarity matrix is reshuffled using each of the corresponding optimised sequences, which produces one image per sequence. For each image, CV is applied with N different sets of parameters; each application produces a collection of families of elements, thus producing a pool of N collections per image. In the next step, SNR is applied to each of these pools, producing a single collection, thus at this point there are 15 collections, one per image. Finally, this last pool of collections is again given as input to SNR, which yields a single collection of families of elements as the output. SI Fig. : Example of application of the computer vision (CV) algorithm for square detection. The original similarity matrix (year 2021) is reshuffled according to an optimised sequence of elements. Diagonal smoothing is used, in which the diagonal of the matrix is hidden to better show the square patterns. This is followed by standard up-sampling, blurring and padding of the image, to increase the resolution and remove the sharp edges coming from individual pixels in the original similarity matrix. Finally, edges are detected on the resulting image using Canny's algorithm, and square shapes are detected. These shapes are filtered, so that final results are squares, lying on the diagonal, whose size corresponds to no more than 20 elements. SI Fig. : Statistical noise reduction algorithm (SNR) for collections of sets. The goal of the algorithm is: given an input pool of collections of families of elements, produce a single collection of families, which results from considering the more statistically relevant features of the families in the input pool of collections. In a first step (a), for each set A ij in collection C i , a new collection {∼ A ij } is assembled, which contains the most similar sets found in every other input collection; similarity between sets is assessed through the Jaccard/Tanimoto similarity . Such collection is then, in step b, reduced to a single representative set, which contains every element that is contained in at least 50% of the sets in {∼ A ij }. Such new representative set takes on the role of A ij . For every newly created collection, all duplicate, empty or single-element families are removed (c). The result is a new pool of collection of families, which is then used as a new input a number M of iterations. In last step e, all collections are merged into a single one, and duplicates, empty or single-element sets are removed again. The output is a single collection of sets, which captures the most representative features of the pool of collections given as input.