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I want to export an animation for polar plot $r=\cos 2\theta$, instead of directly using Animate. But I want a table of snapshots: movie = ParallelTable[...] and a point that produce its animations like to this question. Then export it to my favorite animated graphics format, e.g.: Export["rose,gif", movie]. How can I do it?
I want a gif like this, merely with red point and without the circle and blue line of course for $r=\cos 2\theta$.