We're comparing a power 8 version of the generlized Mandelbrot formula (Zn+1=Zn^k + C, with k=8) against a power-2 quaternion Julia.

In the epilogue, the author admits that there's less variety in the Mandelbulb-8 than even in the classic Mandelbrot.

The common Mandelbrot set is really a 2-dimensional slice of a 4-dimensional object identified by both the combination of the complex numbers Z0 and C in the canonical Zn+1 = Zn^2 + C. The mandelbrot set lives in the plane where Z0 = 0 + 0i, while the Julia sets live on infinitely-many-squared orthogonal planes in the remaining two dimensions, each one intersecting Mandelbrot's plane in a single point of complex coordinates C.

Visualizing this hyperspace monster was made easy by POV-Ray. It took my computer two week of computation to render 80 seconds of animated 3D slices of a the quaternion. Check out the scene source.

/me looks forward for a real-time Julia4D explorer.