A simulation of the Poisson process, built using Processing.
The process models random events occuring in continuous time given that:
- Events occur on their own
- The average rate of events happening remains constant
- Future events have nothing to do with ones which have happened
A process has average rate such as 
per minute. Number of events in t minutes is the discrete random variable X, where 
. The time you have to wait between events follows an exponential distribution 
.
The simulation works by obtaining a waiting time between each event, through making independent observations on the random variable 
. We can do this by solving:
where u is a random observation on the uniform distribution U(0,1). With the exponention distribution this means solving
which ends up with
Each time an event is fired, t is recalculated.