How can an equation for the following curve be derived?
$$r=(1+0.9 \cos(8 \theta)) (1+0.1 \cos(24 \theta)) (0.9+0.1 \cos(200 \theta)) (1+\sin(\theta))$$
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It can be made intuitively out of the following observations:
Finally, all of this points to this
The remaining factors, which have much smaller periods, and expand/contract the radio much less, are there just to make the "borders" looks less regular.
You may do the same as other answer did in details by Maple: