I have plotted all 8 "spirals " of the form 4 : ( +-t^+-1/t), 4: (+- 1/t)^+-(t) in polar coordinates and there are certainly interesting forms , crossing points, and regions.

I do not know how to get image in here, but it is in the atachment.

I do not know how to get image in here, but it is in the atachment.