  Techniques are developed for exploring the complete space of intersecting
brane models on an orientifold. The classification of all solutions for the
widely-studied T^6/Z_2 x Z_2 orientifold is made possible by computing all
combinations of branes with negative tadpole contributions. This provides the
necessary information to systematically and efficiently identify all models in
this class with specific characteristics. In particular, all ways in which a
desired group G can be realized by a system of intersecting branes can be
enumerated in polynomial time. We identify all distinct brane realizations of
the gauge groups SU(3) x SU(2) and SU(3) x SU(2) x U(1) which can be embedded
in any model which is compatible with the tadpole and SUSY constraints. We
compute the distribution of the number of generations of "quarks" and find that
3 is neither suppressed nor particularly enhanced compared to other odd
generation numbers. The overall distribution of models is found to have a long
tail. Despite disproportionate suppression of models in the tail by K-theory
constraints, the tail in the distribution contains much of the diversity of
low-energy physics structure.
