We describe algorithms to compute self-similar measures associated to
iterated function systems (i.f.s.) on an interval, and more general
self-replicating measures that include Hausdorff measure on the
attractor of a nonlinear i.f.s. We discuss a variety of error
measurements for these algorithms. We then use the algorithms to
study density properties of these measures experimentally. By
density we mean the behavior of the ratio $\mu(B_r(x))/(2r)^\alpha$
as $r \rightarrow 0$, were $\alpha$ is an appropriate
dimension. It is well-known that a limit usually does not exist.
We have found an intriguing structure associated to these ratios that
we call density diagrams. We also use density computations to
approximate the exact Hausdorff measure of the attractor of an i.f.s.