I put these graphs on a separate web page because loading them could be a problem. The files total more than 1.1 megabytes.

r=cos(3) This is a three-leafed rose. Please note that the graph shows one sweep, as goes from 0 to 2Pi. The rectangular graph, shown here, has three pairs of ups and downs. The polar trace covers the leaves twice. The six up-and-downs of cos(3) (magically?) reduce to retracings of half of the loops. I hope I made this evident. I introduced some deliberate distortion in the second tracing. Without the distortion, the second tracing could not be seen at all, since the pixels the "point" travels over and colors all had already been colored.

r=cos(4) This "rose" has 8 leaves or petals, and the dynamic way it is traced is weird and wonderful to me. The rectangular graph. to the right, shows four bumps up and four bumps down. There are no retracings of already colored points, so that the wiggles up and down of cos(4) all result in 8 leaves.

Maintained by greenfie@math.rutgers.edu and last modified 5/1/2007.