It feels like as if the English translation should be ' the cat is purring/purrs' then the Danish version would be 'katten spinder' . In this case the cat is making this characteristic humming sound when in relaxed state instead of physically moving around one point.
I don't think purring is it possible meaning here, is it? Turning makes sense and, I even thought of the German expression "spinnen", which suggests that "The cat is crazy" is another possible answer. But purring?
I just looked up purring online and it said 'spinde' or 'snurre' (like schnurren!), but I have to admit 'spinnen' in the German sense immediately sprang to my mind as well, because they really are crazy sometimes!