Horofunctions of infinite Sierpiński polygon graphs

Generalizing works of D'Angeli and Donno, we describe, given an infinite sequence over the alphabet { 0 , … , r − 1 } , with r not divisible by 4, a sequence of pointed finite graphs. We study the pointed Gromov–Hausdorff limit graphs giving a description of isomorphism classes in terms of dihedral groups and we provide a description of the horofunction boundary, distinguishing between Busemann and non-Busemann points.