Are Cellular Automata models related to the Bekenstein bound?

Cellular Automata are discrete models which have a regular finite dimensional grid of cells, each in one of a finite number of states, such as on and off.

There are various scientists that have combined Cellular Automata with the Holographic Principle (like Gerard ‘t Hooft, Seth Lloyd, Paola Zizzi…etc) to describe the universe.

This makes me think that all Cellular Automata models are directly with the Bekenstein bound (https://en.wikipedia.org/wiki/Bekenstein_bound)and thus with holography, but I would need confirmation from an expert.

So, are literally all cellular automata models related with the Bekenstein bound or holography in general?