Can time dilation be explained by limitations on computing power? Are there any ideas of explaining the time dilatation as limits in "computing power"? What I mean is basically that the greater is a concentrated mass, the harder is to "compute" what happens in such system, because more data needs processing (because e.g. more near positioned mass –> more interactions). The same is for speed: if nature is "computing" then having to establish cause-chain of fast objects is simply more demanding – if the "nature" is somehow limited by a time herself (or maybe because greater velocity implies more interactions). This reminds me physical simulations in ODE, Bullet Physics Engine, or other similar package. If the simulation is too demanding, it will appear slow-motion, but only for an outside spectator.
This creates a possible verification experiment: two setups, each having properties, that make general relativity phenomena expected to occur. Then one of the setups should differ in such a way, that would make it more "difficult", more demanding in "complexity" for the suspected "computing machine", but neutral for general relativity theory.
The question is soft, inspired by many theories that try to explain various general questions in physics.
 A: No. For one thing, being closer to a mass, or moving faster, does not automatically make it harder to compute the behavior of a physical system. Also, for fast-moving objects, time dilation is a symmetric effect: observer A will see B's time dilated just as much as B sees A's time dilated, and that would not happen if it were due to a lack of computing power. If it were, there would be a certain absolute rest frame identified by the simulation, in which every observer's time dilation would be a minimum. And of course, the slowing down of simulations that you observe in those programs does not carry into the simulation itself - if there were intelligent beings living in the simulation (if that is possible), they wouldn't notice anything different.
A: Let's say there's a radio tower 1 mile ahead of you and 1 mile to your left.
Now turn 45 degrees to your left.
There is now a radio tower about 1.41 miles ahead of you.
Time dilation is no more exotic than this.  It arises from a generalization of rotational invariance, as applied to spacetime.
