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We investigate the occurrence of exotic structures in the outermost layers of neutron stars within the framework of the microscopic DYWAN model. In this dynamical description, starting from an initial crystal lattice at subnuclear densities, the nuclear system self-organizes with no assumption of final shapes. The model is a ETDHF-like approach in which the numerical treatment makes use of wavelet techniques. In the present work we focus on the study of cold matter in a pure mean-field description in order to explore the evolution of the system towards a multiple low-lying energy configuration corresponding to the different material shapes. These structures are found to be embedded and are studied in terms of a phase diagram. The sensitivity to the equation of state of the structural phases is evidenced. [ABSTRACT FROM AUTHOR]