3D "shadow" of the quaternion mandelbrot

[laser blaster]

I was wondering if the quaternion mandelbrot set was more complex than it appears. If you take a 3D slice of it, the result is only fractal in 2 dimensions, but the real quaternion mandy is 4-dimensional - perhaps there are 3 dimensions worth of fractal complexity hiding in it, that can be revealed with the right visualization method. Well, that was how my thinking went, anyway.

So my idea was, instead of taking a 3D slice of the 4D shape, to project the shadow of the 4D object into a 3D space. Rendering such a visualization requires a brute force search across a 2-dimensional space, for each pixel. But GPU rendering is fast, and I have a powerful GPU, so I gave it a go in Fragmentarium. The initial result looked almost identical to the standard lathed quaternion brot. Adding a rotation to the 4d bulb gave different results, but none of them looked exciting. Whipped cream everywhere.

So, pretty much the whole idea was a failure, haha. I thought someone might be interested to hear about my experiment, though. Here's a picture.

[Roquen]

There isn't.  The math works out to be a surface of revolution around one dimension so no projection will work out to be interesting.