The movie at left is a simulation from the Propp-Wilson algorithm of the monotone two particle contact process. The site colors are defined as follows:
| = 1-, empty site which can become occupied by the native species | |
| = 1+, occupied by the native species | |
| = 2-, empty site which can become occupied by the foreign species | |
| = 2+, occupied by the foreign species |
Species 1 and 2 are interpreted as the native and foreign species respectively. With the parameters used here, it is apparent that the invasion occurs. The boundary conditions are such that the left side is a fixed column of 2+'s and the right that of 1+'s. These boundary conditions can be changed and are made such to reflect a constant source of each species.
With the exception of the boundary conditions, the top movie is started from the state where all sites(16 x 16) are of the 1- type, and the bottom movie shows all 2+'s. This represents the lower and upper extremal states for this process respectively. Then we run the Propp-Wilson algorithm and couple both states until they coalesce. This outputs a final state which is an exact sample from the stationary distribution. On close inspection it can be seen that in the last frame, both movies as exactly the same.
Movie ControlsFirst, this movie is a flash object, so your browser may give you some kind of activeX warning; you will have to allow the content. Then you will probably have to click on the movie to activate the controls. The button descriptions are given below for ease of use.
