What does it mean if the quaternion julia set for a particular constant is connected, but the standard complex plane julia set slice of it isn’t?
One three dimensional slice of a quaternion julia set looks path-connected:
But if we slice it on the complex plane, we see
That in the complex plane alone, there is nothing but Fatou dust:
additional: there has been some work on the connectedness locus of quaternion julia sets. (page 2), but you don’t see the mandelbulbing community actually paying attention to it just yet.