Traversal Languages Capturing Isomorphism Classes of Sierpinski Gaskets

We consider recursive structural assembly using regular simplexes such that a structure at every level is obtained by joining d + 1 structures from a previous level. The resulting structures are similar to the Sierpinski gasket. We use intersection graphs and index sequences to describe these structures. We observe that for each d > 1 there are uncountably many isomorphism classes of these structures. Traversal languages that consist of labels of walks that start at a given vertex can be associated with these structures, and we find that these traversal languages capture the isomorphism classes of the structures.