   how might continuous time be coded??
  I'm trying to implement probabilistic events for a simulation. Each time an event happens I want to update() each particle in a simulation. But these events are probabilistic: say an event happens by a poisson or exponential distribution (or something similar). If the simulation runs at , these events are constrained to occur only at . Clearly, a minuscule  would suffice, but is there another way?(expert mode: I also need a discrete-time graphics engine to work in parallel to this continuous-time simulation)   
  Even though events can only processed at certain intervals, the math can still be written to use a continuous timeline.  For instance, if you determine that some event will take place at some point in the future (using the exponential distribution for instance), then you wait until you reach a frame that just exceeds that time.  So if the last frame happened at time 't', and this frame is happening at time 't+Δ', and you know the event took place within that delta (let's say at 't+ε' where ε < Δ), then you can process the event during this frame, but perform all the math as though the event took place at 't+ε' on the continuous timeline.   