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4(a)] to the case of f =1 / 6 [Fig. 5(a)], one can find that the orbital magnetization in these two fields have a relation 

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This conclusion is a combined exhibition of the above mentioned symmetries (ii) and (iii) in the Hofstadter energy spectrum. 

We have known that the topology of the energy spectrum of the 2D lattice system arises from the competition between the periodic potential-induced level broadening and the mag- netic field-induced level discretization. Once the external magnetic field changes, the topol- ogy of the energy spectrum also changes, which results in the simultaneous prominent vari- ation in the magnetization of the 2D system. The above discussions on the magnetization for different fields f =1 / 4, 1 / 3 and 1 / 6 are typical examples. Now a question is put forward: 

