We characterize fractal chordarc curves in Euclidean space by the fact that they remain bilipschitz homogeneous under inversion. We illustrate this result by constructing two examples. The techniques used in these constructions provide a means of calculating various dimensions of bilipschitz homogeneous Jordan curves.
"Bilipschitz homogeneous Jordan curves, Möbius maps, and dimension." Illinois J. Math. 54 (2) 753 - 770, Summer 2010. https://doi.org/10.1215/ijm/1318598680