Why Universe must be a Cellular Automata?

I think Universe must be a Cellular Automata operating at Planck scale.
(If so failure of GUTs/String Theory etc would not be surprising.)

Some reasons to consider:

Universe needs to be computable why because it is clearly a mathematical structure and it is dynamic so it should be doing calculations.
That also means no real infinities anywhere (infinities break calculations in computers (unless added as special, non-natural treatments)).
So center of BHs or size/scale of 4 dimensions cannot be infinite.
Also if Universe doing calculations it means it is some kind of computer and CA are the simplest (thus the best) candidates.

And the reason why it must operate at Planck scale is because
known laws of physics indicate that is their limit.
It is where they breakdown.
There is absolutely no way to measure a distance shorter than Planck length and a duration shorter than Planck time.
(This means when measured using Planck length as the unit all distances are integers
and when measured using Planck time as the unit all durations are integers.)
That means if Universe is a CA than Planck length must be the size of its cells
and Planck time must be its unit of time steps.
(So every cell would update at each Planck time step.)

If Universe is a CA then it means Quantum and Relativity are its emergent properties.
If this is hard to believe then realize chemistry is the emergent property of quantum
and biology is the emergent property of chemistry.
Notice that trying to use quantum to predict chemistry or
trying to use chemistry using quantum and vice versa are really hard problems!
Also notice when you moving from quantum to chemistry, chemistry to biology back and forth
scale changes exponentially (compare size of a particle with sizes of atoms/molecules,
compare their sizes with sizes of cells/organisms).
(Actually organisms are the emergent property of cells.)
This implies when you go from quantum to underlying TOE, size must get smaller exponentially again.
(So strings are not small enough! :-)

To see how powerful even the simplest CA are consider that
emergent properties of Conway's Game Of Life studied for decades
and I think its full range of different behaviors still unknown (could it be infinite?).
There is another very simple CA called FHP that creates Navier-Stokes behavior at macro scale.
(Today a little more advanced CA called LBM is used to simulate all kinds of liquids.)

If Universe is a CA then considering entanglement (non-local interactions between quantum particles)
for example, it is possible to deduce at least some of the properties it must have.
Another property it must have is conservation of energy (which is really conservation of information (states of the CA)).

I think the best expert on CA today is Stephen Wolfram who also thinks Universe must be a CA.
But as far as I know the idea first proposed by a German computer pioneer named Konrad Zuse.