We would like to simulate events in a virtual world. Our world has time and three cell species (A, B, C).

We can find statistically measure mean time between two event of the same kind.

In our world we have two kind of events: a cell born and a cell die.

Our measured mean values are: Every 5 seconds a new cell of type A is born. Every 30 seconds a cell of type A dies. Every 15 seconds a new cell of type B is born. Every 15 seconds a cell of type B dies. Every 30 seconds a new cell of type C is born. Every 45 seconds a cell of type C dies.

We consider that the birth of a cell is an event that occur continuously (i.e. we do not consider things like seasons.) and independently (i.e. the birth of one cell do not affect the birth of another cell.) at a constant average rate.

This birth process of our cell is called a Poisson process and use and exponential distribution to describe the time between two event (two cell birth).

We are going to use an homogenous type of Poisson process (the parameter lambda is fixed).

The parameter lambda is called the rate parameter and describe the the expected number of events that occur per unit of time.

Lambda its equal to 1 devided by the desired mean.

Programmatically we could use a timer or incorporate that in the main loop of the game.

Increasing lambda will diminish the likelyhood of a manifestation of an event.

Readings:

- This article is loosely inspired by this
- Aaaa