To understand the probabilistic relation between a site's (block) opening and percolation of the system.
I have approached the problem in two ways. Both ways indicate special properties of percolation.
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Probabilistic Opening of Sites
Here, the procedure goes as follows:- Each site has a probability (p) of being opened.
- We iterate through each site and finally check whether the system percolates or not.
Plot: (Probabilty of Percolation) vs (Probability of a Site being Opened)
Examples.
Lattice Size : 40 Probability : 0.4
Lattice Size : 40 Probability : 0.6
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Random Opening of Sites
Here, the procedure goes as follows:- We start with a completely closed site.
- Now, randomly pick and open sites, till the system percolates.
- After percolation we check how many sites have been opened.
Surprisingly, the no. of nodes opened can always be approximated to a good level. There is a high probability that count opened sites is near to threshold ratio.
Examples.
Lattice Size : 40
Lattice Size : 60
