  We study the nodal set of eigenfunctions of the Laplace operator on the right
angled isosceles triangle. A local analysis of the nodal pattern provides an
algorithm for computing the number of nodal domains for any eigenfunction. In
addition, an exact recursive formula for the number of nodal domains is found
to reproduce all existing data. Eventually we use the recursion formula to
analyse a large sequence of nodal counts statistically. Our analysis shows that
the distribution of nodal counts for this triangular shape has a much richer
structure than the known cases of regular separable shapes or completely
irregular shapes. Furthermore we demonstrate that the nodal count sequence
contains information about the periodic orbits of the corresponding classical
ray dynamics.
