The 3D analogue of the Julia set fractal is the quaternion fractal. Since it is rather hard to draw 4 dimensional objects, one needs a way of rendering 4D quaternion fractals onto a 2D screen. The approach used here is to intersect the 4D solid with a plane.  In essence, this makes one of the quaternion components dependent upon the other three. To get a feel for the true nature of the quaternion fractal one needs create a whole series of slices along an axis perpendicular to the slice plane. This is the same as what one does when drawing contour lines to visualize a landscape, where each contour represents a slice of the landscape by a plane perpendicular to the vertical axis. By "stacking" the contours together we gain an appreciation of the surface. Unfortunately, in the case of a 4D object we need to stack 3D solid objects along a 4th axis, which is a little more difficult for our limited 3D visual system. The animation above shows the 3D slices as the cutting plane moves along one of the quaternion axes. Get the code