I never did like hypercomplex numbers and quaternions very much. Neither 
of them are true number fields, and the Julia sets they produce are just 
slightly modified surfaces of revolution.

The complex cubic Mandelbrot set uses only complex arithmetic - a true 
number field - and produces a 4D image that has genuine detail in every 
direction. The resulting images look much more "natural" to my eyes, 
whichever plane you slice it in.

As you say though, this object is not widely known.

(And there's no way you'd ever make a building out of it. It's far too 
impractical...)

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