Studies based on ab initio density functional theory show that the modulated structures of BiO surfaces of cuprate Bi2212 superconductors are spontaneously formed and closely related to the reconstructions of BiO surfaces. The reconstructions of BiO layers occur both on the surface
and in the bulk, accompanied with the formations of BiO-zigzag chains and Bi2O2 quadrilaterals. The structural modulations of the BiO surface are along the b axis, perpendicular to the BiO-zigzag chains along the a axis. Our calculations provide a unified
understanding of the formation of modulating structures in Bi2212. Another interesting result is that electronic structures of BiO surfaces are significantly influenced by the CuO2 layer beneath because of the structural modulations and reconstructions.