[graphviz]

This is interesting and a little bit entertaining.

There has been excellent work on taxonomies for data visualization. Tamara Munzner's book "Visualization Analysis and Design" is a good starting point.

There has been excellent work on identifying "dimensions" or properties of data visualization. Lee Wilkinson's "Grammar of Graphics" is a landmark. You could search backward to find Bertin's Semiology of Graphics, or forward to find ongoing work like UW's Vega https://idl.cs.washington.edu/papers/vega-lite/

Some of this work might somewhat capture the properties of a periodic table to organize a catalog and even support further discovery.