A percolation model was constructed using the Python programming language in order to investigate the percolation threshold for a two- and three-dimensional continuum model by examining several probability graphs created by the programme. Probability graphs were produced for various disk radii, and the percolation thresholds for a two- and three-dimensional continuum model were calculated. The results also indicated that there is a very sharp increase in the probability of forming a spanning cluster at the percolation threshold for a large system. We subsequently estimated the fraction of the total area occupied by the disks at the percolation threshold.
Python 2.x is required to run the scripts (except for those with name beginning with 'ODE_').
Create an environment using conda as follows:
conda create -n python2 python=2.xThen activate the new environment by:
conda activate python2
Figure 1: Two-dimensional model showing disks generated using the script provided. A spanning cluster is formed.
Figure 2: Three-dimensional model of Fig. 1.
Figure 3: Two-dimensional model showing disks generated using the script provided. No spanning clusters is formed.
Figure 4: Three-dimensional model of Fig. 3.
Figure 5: Probability plot with various disk radii.
