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Long observational series for bipolar active regions (ARs) providesignificant information about the mutual transformation of the poloidal andtoroidal components of the global solar magnetic field. The direction of thetoroidal field determines the polarity of leading sunspots in ARs in accordancewith the Hale's polarity law. The vast majority of bipolar ARs obey thisregularity, whereas a few percent of ARs have the opposite sense of polarity(anti-Hale ARs). However, the study of these ARs is hampered by their poorstatistics. The data for five 11-year cycles (16-18 and 23,24) were combinedhere to compile a synthetic cycle of unique time length and latitudinal width.The synthetic cycle comprises data for 14838 ARs and 367 of them are theanti-Hale ARs. A specific routine to compile the synthetic cycle wasdemonstrated. We found that, in general, anti-Hale ARs follow the solar cycleand are spread throughout the time-latitude diagram evenly, which implies theirfundamental connection with the global dynamo mechanism and the toroidal fluxsystem. The increase in their number and percentage occurs in the second partof the cycle, which is in favour of their contribution to the polar fieldreversal. The excess in the anti-Hale ARs percentage at the edges of thebutterfly diagram and near an oncoming solar minimum (where the toroidal fieldweakens) might be associated with strengthening of the influence of turbulentconvection and magnetic field fluctuations on the arising flux tubes. Theevidence of the misalignment between the magnetic and heliographic equators isalso found.

Synthetic solar cycle for active regions violating the Hale's polarity law