I'm not high right now I swear I just had this thought going through my head for a while.
Imagine you had an Eve online (never played) style space game. There are 1000 servers, organized in a grid 10x10x10. Each server is simulating a region of space corresponding to their grid position, and connected via a network link only to the servers right next to it, so as to facilitate traveling between them.
The game is populated by a bunch of bots flying around shooting each other or whatever they're doing. If too many bots happen to be on the same server, it gets overwhelmed, everything on this one specific server slows down to slideshow levels.
I posit that, over time, the bots would tend to get stuck in this laggy region of space. If they fly around randomly, they'd encounter the laggy region of space eventually, and it would take them a lot longer to get out again.
Furthermore, the neighboring servers might also slow down, to a lesser degree, because they have to wait for the laggy server which is unable to respond quickly when handing over bots.
The observable result would be (a) clumping, like how matter clumps together in the universe due to gravity, and (b) time would seem to slow down in the clumped up area, like it does in the theory of relativity.
(a) At a sufficiently large scale, like trillions of servers and bots, this might look like a large scale attracting force. I can even imagine that two large bots swarms, flying past each other, might get stuck more towards their common center point, effectively creating a kind of orbital mechanic. Though maybe not, you'd have to simulate this to see if you could make this happen.
(b) The bots in the clumped up area, being bots simulated by the overwhelmed server, would not notice that time has slowed locally. But if you had two bots, one flies around the empty parts of space, while the other flies into the clump and then comes back out, it would seem like more time has passed for the bot that was in empty space the whole time.