Imagine the grid where every pixel is open with some probability p. What is the probability to get from left side of the grid to right via open pixels (site percolation)?


Result:
Probability to enable a pixel (0 to 100):
Pixel size:


Note: If you want to get an idea of critical percolation threshold (high probability that long-range connectivity occurs), it is possible to run multiple iterations for all probabilities (0 to 100) and calculate how many times long-range connectivity occured. In order to do it, open developer’s console in browser and execute:

>> simulate(20); //for every input prob runs 20 iterations to calculate prob of long-range connectivity
probability to enable pixel = 0 probability of long-range connectivity = 0
probability to enable pixel = 0.01 probability of long-range connectivity = 0
....
probability to enable pixel = 0.59 probability of long-range connectivity = 0
probability to enable pixel = 0.6 probability of long-range connectivity = 0.15
probability to enable pixel = 0.61 probability of long-range connectivity = 0.35
probability to enable pixel = 0.62 probability of long-range connectivity = 0.7
probability to enable pixel = 0.63 probability of long-range connectivity = 0.9
...