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Pattern formation
On this page we present some preliminary results for the pattern formation model.
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Consider a system of identical particles in a 2D space. There are two types events that can occur:
- a death of a particle - the particle is removed from the system,
- a birth of a particle - one of the existing particles causes the creation (birth) of the new particle which is added to the system.
The death has a constant rate d - the probability that the particle dies is the given moment is constant. This means that particles' lifetime is has an exponential distribution with some expected lifetime 1/d.
The probability that given particle gives birth to another one is dependent on other particles, especially on those in the proximity of the both parent and child particles. A particle can not give birth if within the radius R around the particle there are more than C other particles. Above this threshold the particle might give a birth with the constant intensity b.
The placement of the offspring particle was drawn from the 2D Gaussian distribution centered around the parent particle and standard deviation equal to r in each direction.