{{Percolation Simulation}}
Given an <math>M \times N</math> rectangular array of cells numbered <math>\mathrm{cell}[0..M-1, 0..N-1]</math>assume <math>M</math> is horizontal and <math>N</math> is downwards. 

Assume that the probability of any cell being filled is a constant <math>p</math> where
: <math>0.0 \le p \le 1.0</math>

;The task:
Simulate creating the array of cells with probability <math>p</math> and then 
testing if there is a route through adjacent filled cells from any on row <math>0</math> to any on row <math>N</math>, i.e. testing for site percolation.

Given <math>p</math> repeat the percolation <math>t</math> times to estimate the proportion of times that the fluid can percolate to the bottom for any given <math>p</math>.

Show how the probability of percolating through the random grid changes with <math>p</math> going from <math>0.0</math> to <math>1.0</math> in <math>0.1</math> increments and with the number of repetitions to estimate the fraction at any given <math>p</math> as <math>t >= 100</math>.

Use an <math>M=15, N=15</math> grid of cells for all cases.

Optionally depict a percolation through a cell grid graphically.

Show all output on this page.