  The Sullivan dictionary provides a beautiful correspondence between Kleinian
groups acting on hyperbolic space and rational maps of the extended complex
plane. An especially direct correspondence exists concerning the dimension
theory of the associated limit sets and Julia sets. In recent work we
established formulae for the Assouad type dimensions and spectra for these
fractal sets and certain conformal measures they support. This allows a rather
more nuanced comparison of the two families in the context of dimension. In
this expository article we discuss how these results provide new entries in the
Sullivan dictionary, as well as revealing striking differences between the two
settings.
