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I'm just looking for a name for this type of plot, which is time vs real part vs imaginary part shown as a space curve.

Complex exponential:

complex sinusoid

Used to explain chirplets:

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Complex Morlet wavelet shown this way:

enter image description here

instead of being shown as two plots:

enter image description here

enter image description here

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I've seen the inverse of your situation, where a given space curve's projections on the coordinate planes are plotted along with the space curve itself, referred to as a "shadow plot". –  J. M. May 12 '12 at 16:33
    
Another example: pacifict.com/Examples/Gallery42.html "Complex functions of a real parameter A complex function of a real parameter can be drawn as a curve in 3D." –  endolith Jun 30 '12 at 1:31
    
Another example: ccrma.stanford.edu/~jos/st/… –  endolith Jan 16 '13 at 2:50

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