  In this article we extend on work which establishes an analology between
one-way quantum computation and thermodynamics to see how the former can be
performed on fractal lattices. We find fractals lattices of arbitrary dimension
greater than one which do all act as good resources for one-way quantum
computation, and sets of fractal lattices with dimension greater than one all
of which do not. The difference is put down to other topological factors such
as ramification and connectivity. This work adds confidence to the analogy and
highlights new features to what we require for universal resources for one-way
quantum computation.
