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I'm a first year physics student, and one of my assignment for my programming class is about percolation. I need to create some disks randomly distributed in an area (this is a 2-D), and then by varying the density of the disk, I need to figure out the percolation threshold such that the two sides of the square area is connected by the clusters of disks.

The worksheet also suggests some extension to the essential tasks, like making it 3-D and including disks with different radius, both of which I manage to do. But I'm wondering if there are some physical systems or phenomena that I can actually simulate using this simple model. Since I need to submit a report by the end, I expect I can use my model to simulate something to get some data (density, radius of disks, etc), then I can compare the results I get with some accepted value in literature to see how well my model does (which is similar to what I usually do for my first-year lab).

Are there any particular theories or models that I can test or simulate? Any recommended books for me to learn more about the basic of percolation?

The attached file is what I get using my program (300 disks with r=0.03 and 400 disks with r=0.02) for your reference.

thanks

The worksheet also suggests some extension to the essential tasks, like making it 3-D and including disks with different radius, both of which I manage to do. But I'm wondering if there are some physical systems or phenomena that I can actually simulate using this simple model. Since I need to submit a report by the end, I expect I can use my model to simulate something to get some data (density, radius of disks, etc), then I can compare the results I get with some accepted value in literature to see how well my model does (which is similar to what I usually do for my first-year lab).

Are there any particular theories or models that I can test or simulate? Any recommended books for me to learn more about the basic of percolation?

The attached file is what I get using my program (300 disks with r=0.03 and 400 disks with r=0.02) for your reference.

thanks