The Mandelbrot Set itself is a(t least usually a) simple yes/no classification to a point on the 2 dimensional complex plane as to whether it is inside or outside the set.

... but there are many possible values/points in that set, and upon closer inspection of the intermediate computations involved, there's an entire "ecosystem" involved.  Imagine instead that the binary black/white Mandelbrot set is instead the 2-D "volume" of a planet with an interconnected living structure both internal and external to it.

I almost couldn't resist posting this because I felt like he's practically doing a tease - I DID find Darth in the Mandelbrot Set (or at least a(n accidental) variant of the "Buddhabrot" fractal)

The Dark Side of the Mandelbrot Set

Along with that there popped up fish, ant heads with mandables, ghost from Ghostbusters, Nazi helmets, rainbow wombs and ... well it seems to depend a lot upon how the information is projected.

Someone invented and interesting 3 dimensional extension of this (though I assume other 3D extrapolations are possible).  My Avatar icon is an example but to go beyond that, here's a stereoscopic flythrough (cross your eyes to see it as a 3 dimensional image - might take some practice - don't get stuck with your eyes crossed! LOL) of a Mandelbulb environment with "realtime" changes in parameters so that the terrain morphs as well.