We describe the surface topography domain in a strained InGaAs/AlGaAs system on the GaAs (311)B substrate during metalorganic-vapor-phase-epitaxial growth. The surface rearrangement resulting in the formation of nanostructures seems to belong to a Turing-type self-organization phenomenon that results from a spontaneous symmetry-breaking instability in nonlinear dynamical systems. The unique surface morphologies on the high Miller index faces suggest a novel fourth growth mode due to Turing-type self-organization. ©1997 American Institute of Physics.