When branch points are present in laser beam wavefront during the propagation in turbulence, the adaptive-optics system for atmosphere turbulence compensation will be degraded greatly. The number of branch points was computed by four-dimensional code. By choosing different phase screen number, grid size and grid step, the variation of branch point number with turbulence strength in distorted optical fields was emulated. The result indicates that branch points cannot be detected in the region of weak turbulence. In the intermediate region between the weak and the strong turbulences, the branch points begin to appear, and the number of branch points grows rapidly at the outset of this region, almost linearly. When the turbulence strength continues growing, the rapid growth of the branch point number is replaced by a slower but nonlinear increase. In the end, the branch point number reaches a saturation state. In addition, the branch point number and its evolvement are different in different propagation conditions.