Evolving lines with mirror effect I would like to create evolving lines similar to those in this sequence (starting at 0:28): 
                
            

I know how to reveal lines, but I struggle to make the line moving so smoothly while continuously increasing its width (narrow at the tip and slowly widening).

Could you please give me some tips on how to do this in After Effects? Thanks!
Try to use 3d Stroke. 

                
            
The taper parameter should help you.