Mathematical analysis of Paleodictyon: a graph theory approach

The graphoglyptid ichnogenus Paleodictyon has been alternatively interpreted as a foraging or farming trace; as a subsurface burrow for the habitation of one or more unknown organisms; the remains of a xenophyophore; and as the result of modular growth of an unknown organism. Graph theory and analysis of the geometry of the regular ichnospecies suggests that if the elements of Paleodictyon are interpreted as tunnels, then they are of extraordinary length relative to the size of any likely solitary tracemaker. In addition, because each vertex of the mesh is of degree three, any possible path through mesh requires revisiting in order to travel through the entire network; this makes the minimum path length even longer. These results suggest that it is unlikely that Paleodictyon is the result of subsurface burrowing.