Here you can discover/verify the answer to a well-known problem that may seem interesting to mathematicians but has only been solved by programmers. There are several variants of the problem, one of which is:
In a system of randomly distributed insulating and metallic materials, what fraction of the materials need to be metallic so that the composite system is an electrical conductor?
Although there is no mathematical proof for it, the answer for a square grid is known to (magically) converge to 0.592746... In the grid below, the sites will randomly open until the entire system percolates, which will happen when a certain fraction of the sites are open. As you repeat the experiment and increase the grid size, you will see that the running average of that fraction gets closer and closer to 59.3%.
Site Count: 256
Open Site Count: 0 (0%)
Here you can perform a series of independent experiments on a grid size of your choice and take a look at the results.