Percolation theory describes the physics and mathematics of long-range connections in random systems and is applicable to a broad range of physics systems including conductivity, porosity, and polymers, but can also be used to analyse diverse systems such as forest fires, disease epidemics, and social networks.

This application uses Python (libs: Matplotlib, Scipy and Numpy) to build a percolation model using a 2D continuum of a uniform, random distribution of disks. The code below allows for (a) the distribution of disks to be initially plotted; (b) clusters of overlapping disks to be identified; (c) a long range connection between these clusters spanning the entire continuum to be identified and subsequently plotted.

The application was initially used to model a simple phase transition (using water), and later used to model the degrees of freedom between two given individuals in a social network (using Twitter).