I'm making an app that needs to generate deterministic random events. They need to be deterministic so I can compute which events happened when the app was closed. Basically, my events are points scattered along a line and I need a function f(a,b) that tells me the number of points between the locations a and b. I could discretize my line and randomly decide whether there is a point at every location using the location to seed my generator, but that seems like cheating. I would like to know if there is a more elegant way to do this that uses real numbers.
I believe this problem may have some connections with the Poisson distribution.