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So if you consider a 4D space {Zr,Zi,Cr,Ci} and the set of points such that iteration Z = Z * Z + C remains less than a bailout value (using complex math), you've got a classic fractal.  If you take a two dimensional slice by setting the images X & Y coordinates to two of those four axes, and leave the other two set to 0,0 you can get six different images:

Zr,Zi (standard Mandelbrot)


Cr,Ci (standard Julia Set, and since the other two values are 0,0 we end up with a circle)


Cr,Zi


Ci,Zi


Cr,Zr


Ci,Zr


All of these were rendered with the same "view point" (centered at the origin), with the inside using a "min" coloring, and nice smooth continuos outside coloring.