  Modeling the interior of a planet is difficult because the small number of
measured parameters is insufficient to constrain the many variables involved in
describing the interior structure and composition. One solution is to invoke
additional constraints based on arguments about how the planet formed. However,
a planet's actual structure and composition may hold clues to its formation
which would be lost if this structure were not allowed by the initial
assumptions. It is therefore interesting to explore the space of allowable
compositions and structures in order to better understand which cosmogonic
constraints are absolutely necessary. To this end, we describe a code for
generating random, monotonic, density distributions, rho(r), that fit a given
mass, radius, and moment of inertia.
  Integrating the equation of hydrostatic equilibrium gives the pressure, P(r),
at each point in the body. We then provide three algorithms for generating a
monotonic temperature distribution, T(r), and an associated composition that is
consistent with the rho-P relation, and realistic equations of state. We apply
this code to Uranus as a proof of concept, and show that the ratio of rock to
water cannot be much larger than 2.
