There is at least one relation between the cellular automata and the holographic principle that is mostly historic. t'Hooft proposed in the following paper -- which is often considered as one of the origins of the idea of the holographic principle-- that black holes behave quantum mechanically like a evolving grid of boolean variables (i.e. a cellular automaton).

t'Hooft himself is still proposing these kind of models as a underlying model for quantum mechanics, but the idea of holography in its modern form of the AdS/CFT-duality was developed without any reference to these cellular automata.

The Bekenstein bound is a bound on the amount of entropy (i.e. the number of available microstates) for a system of given volume and energy.

I am not aware that the idea that cellular automata can describe physical systems matured to such an extent that you can actually speak of all these concepts (energy, volume, Hilbert spaces) in the framework of this model.

There is at least one relation between the cellular automata and the holographic principle that is mostly historic. t'Hooft proposed in the following paper -- which is often considered as one of the origins of the idea of the holographic principle-- that black holes behave quantum mechanically like a evolving grid of boolean variables (i.e. a cellular automaton).

t'Hooft himself is still proposing these kind of models as a underlying model for quantum mechanics, but the idea of holography in its modern form of the AdS/CFT-duality was developed without any reference to these cellular automata.

The Bekenstein bound is a bound on the amount of entropy (i.e. the number of available microstates) for a system of given volume and energy.

I am not aware that the idea that cellular automata can describe physical systems matured to such an extent that you can actually speak of all these concepts (energy, volume, Hilbert spaces) in the framework of this model.