  The robustness of connectivity and the efficiency of paths are incompatible
in many real networks. We propose a self-organization mechanism for
incrementally generating onion-like networks with positive degree-degree
correlations whose robustness is nearly optimal. As a spatial extension of the
generation model based on cooperative copying and adding shortcut, we show that
the growing networks become more robust and efficient through enhancing the
onion-like topological structure on a space. The reasonable constraint for
locating nodes on the perimeter in typical surface growth as a self-propagation
does not affect these properties of the tolerance and the path length.
Moreover, the robustness can be recovered in the random growth damaged by
insistent sequential attacks even without any remedial measures.
