A sequence of four 90° dual-rotations through the four-dimensional parameter space of the Mandelbrot fractal. The sequence starts off showing an inverted view of the Buddhabrot where the head of the Buddha is still shown on the top of the screen as usual, but with the insides outside and the outsides in. Infinity has been moved to the center of the screen and the zero origin has been splayed out into infinity.

1. The first step takes the inverted ZrZi plane and transforms it into the CrCi plane by way of a ZrCi⨯ZiCr dual-rotation. Since the rotation happens along "mixed planes" it also has the effect of swapping the screen-space orientations of the real and imaginary components. As a result of this the CrCi plane appears at a 90° angle from upright — real component right to left and the imaginary top to bottom.

2. The second step transforms the CrCi plane (Mandelbrot) into the un-inverted ZrZi plane (Buddhabrot) with a ZrCr⨯ZiCi dual-rotation. This time the rotation takes Zr to Cr and Zi to Ci so the screen-space orientation of real and imaginary is preserved (although the direction of the real-axis ends up mirrored).

3. The third step re-performs the first dual-rotation and with the second 90° real/imaginary mixing we end up with an upside-down Mandelbrot.

4. The fourth step re-performs the second dual-rotation, but this time rotating into the inverted ZrZi space. This rotation completes the sequence and restores the inverted Buddhabrot we started off from!