There are 3 main versions of the Mandelbulb formula - Daniel White's
original cosine version and a "-sine" and "+sine" version, both
suggested by Paul Nylander. Historically the "-sine" version was
preferred due to less "whipped cream" on the z^2+c version but Paul
showed that the "+sine" version is actually more mathematically
consistent though still far from being an algebraic field.
Here's a degree 7 render of the "-sine" version - I prefer the degree
7 to the more commonly rendered degree 8 :)
http://www.fractalgallery.co.uk/mandelbulb_degree_7.html