Thanks everyone for the cat / hula-hoop experiment.
I tried making a circle with a long scarf. Pud completely ignored it. But, like her owner, she is unusually self-absorbed.
It freaked me out slightly, as it looked like a black magic symbol in the middle of my living-room carpet.
I slightly felt an urge to go into the middle

Google says it possibly is a thing. It could, apparently, be because they keep themselves warmest by forming their body into a circle.
This YouTube video is worth a look. The circle gets smaller. But the cat still loves it