The precision parameter is a tolerance used in the determination of whether points are inside or outside the fractal object.
Larger values give more accurate results but slower rendering.
Use as low a value as you can without visibly degrading the fractal object's appearance. The presence of the keywords quaternion or hypercomplex determine which 4-D algebra is used to calculate the fractal. Both of these algebras were discovered in the 19th century. Of the two, the quaternions are much better known, but one can argue that hypercomplex numbers are more useful for our purposes, since complex valued functions such as sin, cos, etc. can be generalized to work for hypercomplex numbers in a uniform way. The basis vectors 1 and i behave exactly like the familiar complex numbers 1 and i in both algebras.