The first in what will probably be a very occasional series on result generation - random or not - to get some of the weirder raw ideas out there for delving into in the spirit of the D1 post.
For the first then, what if dice were a kind of particle of fate?
What if when you roll more than one die and two or more of them end up touching, they annihilate each other, meaning the results aren't counted? Or the smaller result is subtracted from the larger? Or they fuse, so you total the two numbers?
Or maybe some pass beyond knowledge, so if one die ends up at least twice as far from the nearest as that one is from any other, it's ignored? Or maybe it can't be used until another one gets closer? If it rolls off the table the effect in-game could take place on another plane, or the result could show how many dice vanish with it, bleeding potential from the tabletop.
It could also work for interactions between the dice being used by different players, and there's real potential here. If dice stop in contact or strike each other and rebound, there could be a connection in-game. Stopping in contact could mean a result for one player affecting another immediately, but a rebound might see the effect offset in time or space, with the distance between the dice on a line drawn to the roller being direction in time. Positions relative to objects like mugs, notes or terrain pieces could be interpreted in terms of events or locations.
The connections could be allowed alter the nature of the game world, changing established facts and keeping reality in flux.
Could colour make a difference, or the energy put into the roll, or a given number being rolled in a matching hour or minute?
What happens if a die manages to get past the GM's screen?