A summary video showcasing the various four-dimensional orientations of the Buddhabrot with animated transitions. As a visual guide all rendered points are colored based on the c-sample argument (or angle) as measured in its own parameter plane, ie. in the ordinary Mandelbrot orientation (which in the video is referred to as the CrCi orientation). For example, all purple points in all shown orientations originate from the cusp of the main cardioid and all green points originate from the head of the Buddha.

The video starts from the ordinary Buddhabrot orientation – the ZrZi parameter plane is shown fully with the CrCi plane fully hidden. In four dimensions we have a total of six cardinal rotation planes as opposed to the three we are restricted to in our everyday lives. The complete sequence of rotations is described below:

• The first rotation is performed in the ZiCi plane which transforms the imaginary z-components into imaginary c-components. After a 90° rotation we arrive at the ZrCi orientation and another 90° rotation returns us to the orientation we started from. Although, if you pay close attention to the colors you may notice that this is actually a horizontal mirroring of the original orientation.

• The second rotation is performed in the ZiCr plane. After a 90° rotation we arrive at the ZrCr orientation where all imaginary components are hidden with only the real components shown. In this orientation the body of the Buddha clearly traces out a bifurcation diagram. Another 90° rotation returns us to our actual starting point, the unmirrored ZrZi orientation.

• The two prior rotations looked like rotations around an apparent vertical axis in some three-dimensional subspace. The third rotation in the ZrCr plane appears different. Now the Buddhabrot looks as if it is rotating around a horizontal "subspace-axis" ending up in the CrZi orientation. As with the two previous orientations, a clear "discretization" along the c-dependent directions is visible. Returning to the Buddhabrot plane we find ourselves upside down.

• The fourth rotation is performed in the ZrCi plane. The resulting fully imaginary CiZi orientation looks as though it could be a view from directly "above" the Buddhabrot – whatever that even means. Again the luminosity is concentrated in discrete bands. Rotating through the second 90° half gets us back again to our original starting position.

• The fifth rotation is special treat that a four-dimensional space offers us. It is a dual rotation around two independent planes at the same time. In this instance, the planes in question are ZrCr and ZiCi. The effect of the dual rotation is to take us directly from the Buddhabrot orientation to the perhaps more familiar Mandelbrot orientation. Seen in the video this looks as if the Buddhabrot is squeezed into itself as if sweeping all that extra complexity under a very carefully placed rug.

Completing the fifth rotation also completes our journey through the six cardinal planes of the four-dimensional Buddhabrot.

Note that rotations in the ZrZi and CrCi are not shown since they are just ordinary two-dimensional rotations of the Buddhabrot and Mandelbrot respectively. If we were to start from the other orientations they would have their own special flavor though, but that's a story for another video.

The accompanying music is an original composition titled 'Stardust'.