Type "Polar plot 6 curves of the form r = (1 + Sin[2^(k - 1) t]/2^(k - 1)) where k =1, 2, .., 6 and t=0 to 2 Pi each curve should be a different color" into ChatGPT5.

https://chatgpt.com/share/690f675d-c340-8013-b598-41fe487b4e...

It has the nice properties that you can do any number of sets (in theory) and all the boundary intersections are either osculating or perpendicular.