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This paper presents numerical solutions of particular Lemaitre-Tolman modelsapproximating a fractal behaviour along the past light cone, as discussed inpaper I (0807.0866) of this series. The initial conditions of the numericalproblem are discussed and the algorithm used to carry out the numericalintegrations is presented. It was found that the numerical solutions are stiffacross the flat-curved interface necessary to obtain the initial conditions ofthe problem. The spatially homogeneous Friedmann models are treated as specialcases of the Lemaitre-Tolman solution and solved numerically. Extending theresults 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 donot appear to remain homogeneous along the backward null cone, with a vanishingvolume (average) density as one approaches the Big Bang singularityhypersurface. Fractal solutions, that is, solutions representing an averagedand smoothed-out single fractal, were obtained in all three classes of theLemaitre-Tolman metric, but only the hyperbolic ones were found to be inagreement with observations, meaning that a possible Friedmann backgrounduniverse would have to be an open one. The best fractal metric obtained throughnumerical simulations is also analysed in terms of evolution, homotheticself-similarity, comparison with the respective spatially homogeneous case andthe fitting problem in cosmology. The paper finishes with a discussion on someobjections raised by some authors against a fractal cosmology.

On Modelling a Relativistic Hierarchical (Fractal) Cosmology by Tolman's Spacetime. III. Numerical Results