Holographic automata

[JocK]

The entropy S that can be contained in a spatial region is limited by
the surface area of that region such that S/k < A/4 (where A is the
surface area expressed in multiples of the Planck area).

This remarkable result has lead to the conjecture known as 'the
holographic principle' which states that all of the information
contained in a volume of space can be represented by a theory that
lives in the boundary of that region and that takes into acount at most
one degree of freedom per Planck area.

Now my question is: has anyone ever constructed a discrete dynamical
model on a volume V such that the evolution of this model can be
represented by a lower-dimensional disrete dynamical model operating on
the boundary enclosed the volume V?

I know there is such a thing as the AdS/CFT correspondence which states
that a string theory or supergravity defined on some sort of Anti de
Sitter space is equivalent to a conformal field theory defined on its
boundary. This, however, is way too complicated for me. I am interested
in simple models that I can play with and that can be seen as a
realisation of the holographic principle.