  The basins of convergence, associated with the roots (attractors) of a
complex equation, are revealed in the Hill problem with oblateness and
radiation, using a large variety of numerical methods. Three cases are
investigated, regarding the values of the oblateness and radiation. In all
cases, a systematic and thorough scan of the complex plane is performed in
order to determine the basins of attraction of the several iterative schemes.
The correlations between the attracting domains and the corresponding required
number of iterations are also illustrated and discussed. Our numerical analysis
strongly suggests that the basins of convergence, with the highly fractal basin
boundaries, produce extraordinary and beautiful formations on the complex
plane.
