  This paper presents numerical solutions of particular Lemaitre-Tolman models
approximating a fractal behaviour along the past light cone, as discussed in
paper I (0807.0866) of this series. The initial conditions of the numerical
problem are discussed and the algorithm used to carry out the numerical
integrations is presented. It was found that the numerical solutions are stiff
across the flat-curved interface necessary to obtain the initial conditions of
the problem. The spatially homogeneous Friedmann models are treated as special
cases of the Lemaitre-Tolman solution and solved numerically. Extending the
results of paper II (0807.0869) on the Einstein-de Sitter model, to the $K =
\pm 1$ models, it was found that the open and closed Friedmann models also do
not appear to remain homogeneous along the backward null cone, with a vanishing
volume (average) density as one approaches the Big Bang singularity
hypersurface. Fractal solutions, that is, solutions representing an averaged
and smoothed-out single fractal, were obtained in all three classes of the
Lemaitre-Tolman metric, but only the hyperbolic ones were found to be in
agreement with observations, meaning that a possible Friedmann background
universe would have to be an open one. The best fractal metric obtained through
numerical simulations is also analysed in terms of evolution, homothetic
self-similarity, comparison with the respective spatially homogeneous case and
the fitting problem in cosmology. The paper finishes with a discussion on some
objections raised by some authors against a fractal cosmology.
