The first point rotates about the origin with period t = 2*pi tracing out a circle. The second point rotates about the first with a period three times that of the first and the third point rotates about the second with a period five times that of the second or fifteen times
that of the first. The locus generated by the points as they travel around the circle creates the image you see below.
When the frequency multipliers are odd integers you get a locus that is symmetric about the x and y axis.
The image of the inverse function can be obtained simply by rotating the locus ninety degrees, that is, add pi*2 to the phase or just flip the definitions for x and y.
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