How do I emulate MATLAB's comet plot?

frames = Table[
  ParametricPlot[{Sin[12 u] Cos[u], Sin[12 u] Sin[u]}, {u, 0, t}, 
   PlotRange -> {{-1, 1}, {-1, 1}}], {t, .001, 2 Pi, 2.1 Pi/100}]

and then either

ListAnimate[frames]

or

Export["movie.gif", frames]

depending on what you want. The latter yields

You can also do this:

 Manipulate[ParametricPlot[{Sin[12 u] Cos[u], Sin[12 u] Sin[u]}, {u, 0, t}, 
       PlotRange -> {{-1, 1}, {-1, 1}}], {t, .01, 2 Pi}]

You can use Animate, you'll note that I added some options, remove them to see why :)

Animate[
 ParametricPlot[{Sin[12 u] Cos[u], Sin[12 u] Sin[u]}, {u, 0, umax},
  PlotRange -> {-1, 1},
  PerformanceGoal -> "Quality"],
 {umax, 0.1, 2 Pi}]

You can change Animate to Manipulate if you wish to slide back and forth manually as well

Unchecked :

 Needs["NETLink`"]
 m = CreateCOMObject["matlab.application"]

 m@Execute["t = 0:.01:2*pi;
            x = sin(12*t).*(cos(t));
            y = sin(12*t).*(sin(t));
            comet(x,y);"]

First seen this here.