This emerged many years ago in biological models of population growth. Notice that within the chaotic region, there are narrow bands where there is a small, odd number of stable values. This gives the iteration time to settle into the characteristic patterns that constitute the bifurcation diagram, and results in a clean-looking plot. However, using lower values produces interesting results too. Set Filter Cycles to 1 for an unfiltered map.
Beta is used in the bifmay bifurcations and is the power to which the denominator is raised.
Note that fractint normally uses periodicity checking to speed up bifurcation computation. Many formulae can be used to produce bifurcations. He found that the ratios of lengths of adjacent areas of bifurcation were four and a bit. This helped him guess where bifurcation points would be, and saved lots of time. He also went on to tell other scientists.