Hypercomplex 4D Julia Set Passing Through 3D-space

A 4D Julia set of a modification of the quaternions, q(n+1)=q(n)^2+z, where q=a+bi+cj+dk and ii=jj=kk=-1, ij=ji=k, ik=ki=j, jk=kj=i Animation by rotating plane ZX while the object passes 3D-space. Note that the 4D-object itself doesn't change shape; it's just that the 3D cross-section looks different dependent on where in the 4th dimension you take the 3D-section.