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This piece is a representation of a slice of the quaternion Julia set. Quaternions are a sort of supercomplex number with three different imaginary components, so the Julia set in quaternion space is a four-dimensional fractal, which we can only ever see three-dimensional 'slices' of. There are many variations on the quaternion Julia set and many ways to slice it (and you can find several examples here on Shapeways), but they generally have the sort of 'linked hoops' structure that this piece illustrates well.
This piece is approximately 2 1/2 inches (6 cm) long, which is large enough to let some of the finer structure show through in 3D printed plastic, without becoming so large that it uses excessive material to print.