# Percolation Exercises

Percolation theory is the study of the connectivity of networks. If you
take a piece of paper and punch small holes in it at random positions, it
will remain connected if the density of holes is small. If you punch so
many holes that most of the paper has been punched away, the paper will
fall apart into small clusters.
There is a *phase transition* in percolation, where the paper first
falls apart. Let *p* be the probability that a given spot in the
paper has been punched away. There is a critical probability
*p*_{c} below which the paper is still connected from top to
bottom, and above which the paper has fallen into small pieces (say, if it
is being held along the top edge).

The computation exercise develops class libraries for creating percolation
networks and breadth-first search algorithms for finding their clusters.
The scaling exercise introduces scaling and critical phenomena methods
for studying the phase transtion for percolation.

### References

### Links

James P. Sethna,
Christopher R. Myers.
Last modified: August 24, 2006

Statistical Mechanics: Entropy, Order Parameters, and Complexity,
now available at
Oxford University Press
(USA,
Europe).