Hierarchical structural symmetry of periodic islands embedded in the chaotic region of modified optical injection semiconductor lasers (MOISLs) is expounded upon in phase diagrams.The onset of the bifurcation cascade shows remarkable accumulation horizons.Each cascade follows a specific period-adding route.Self-similarities and infinite spiral nestings shrinking beyond a certain point of the periodic hub are revealed to affirm the existence of self-organized distribution of periodicity and chaos in phase diagrams.