one note about quaternion julia sets…

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.

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