  In an orientable surface with boundary, free homotopy classes of curves on
surfaces are in one to one correspondence with cyclic reduced words in a set of
standard generators of the fundamental group. The combinatorial length of a
class is the number of letters of the corresponding word. The self-intersection
of a free homotopy class (that is, the smallest number of self-crossings of a
representative of a class) can be computed in terms of the word. For each of
the free homotopy classes of length twenty on the punctured torus, we compute
its self-intersection number and make a histogram of how many have
self-intersection 0, 1, 2..... The histogram is essentially Gaussian.
