Lots of people have answered or tried to answer this question. I thought I would have an attempt myself. It has to do with a feeling of security. A tape square on the ground provides a boundary. It is not a solid boundary. It is a visual boundary. We know that domestic cats like boxes. They like the feeling of being inside a box. They like it I believe because it makes them feel more secure.
A tape square allows a cat to feel more secure because it replicates a box at an emotional level. If this is correct then it might indicate that domestic cats feel less secure than we believe they do. If you put a tape square on the ground in your home your cat might walk into it looking for that feeling of security.
If this is an emotional response then this behaviour does tell us something about the domestic cat. Either the cat has an imagination to be able to pretend or fool himself that he is sitting inside a box or a solid boundary or he is simply reacting instinctively to a visual image of a square and not rationalizing the fact that it is not a real object. In other words the cat is unable to realise that the tape square is not a real, solid object. That seems unlikely but it may be true. Extending this argument, it could be stated that the domestic cat is programmed from a newborn kitten hood to like the feeling of a solid boundary against them when they nestle against their mother. So they search for this solid boundary pressing against their body.
Cats also like or need a home range. This is normally the boundaries of the house if the cat is a full-time indoor cat. I have a sense though that this is not about a cat looking for territory or seeking a miniature home range. This has been suggested by one or two people. It is far more likely to be about finding a secure place, even a place to hide.
Another aspect of this behaviour is that although we see videos of cats walking into tape squares on the ground or even circles nobody as far as I am aware has carried out a study on this in a scientific way. I say this because we don’t know how many cats walk into these tape squares and how many don’t. So if you had a sample of 100 cats it might be the case that only 20 like to walk into the square while the other 80% totally ignore it.
A debunking video!
And I think that is a very good point to make because I suspect too that the study would debunk a lot of this speculation about domestic cats liking tape squares on the ground. If more than half of observed cats ignored it then we can’t say that cats like to do it. We can’t generalize. It may be that cats who feel slightly insecure because they are timid or the home is unfriendly have a tendency to seek a secure place and therefore walk towards the tape square.
The fact that some cats do it does make me think that cat owners should do all they can to encourage their cats to feel secure because with security you receive contentment and calmness. Making a cat feel secure is a very important gift that a cat owner can give to their cat. One way to do this is to make sure a cat is not stressed in a multi-cat home.
Dr. Nikko Tinbergen is a well-known European Ethologist who studied the behavior of a variety of animal species under more natural conditions than ordinarily found in psychological experimentation. In investigating the mating behavior of the stickleback fish, he noticed that males are attracted to gravid females whose bellies, swollen with eggs, take on a red color. He called the red belly a “sign stimulus.” Using a number of models, he noted that any object about the size of a female stickleback attracted male sticklebacks. Surprisingly, a disc that was red on the bottom and white on the top elicited a stronger response from the male than did a more accurately shaped model. He called this a “supernormal sign stimulus.” Tinbergen noted similar phenomena in a variety of animal species including birds.
I would suspect that something similar is going on with cats and tape squares. Cats find/build nests where they do their whelping and rearing kittens. Cats seek and occupy small enclosures where they are only facing the world from a reduced angle. Cats are among numerous species that display what is called technically a positive thigmotaxis; that is, they seek to situate themselves where they are in contact with something that presses against their skin. It is possible that tape squares capture important sign stimulus characteristics of a preferred close space to a degree that elicits this behavior.
Scientifically, as entertaining as it may be to do so, to answer this question it is not necessary to conjecture about how the cat feels. Cats naturally seek enclosed spaces. Their search is guided by the presence/absence of salient characteristics of enclosed spaces. It is safe to conclude that a tape square has those characteristics to a degree that causes some cats to approach and occupy it.
Interesting behavior, isn’t it?
Thank you Paul for your excellent information on this. It is the sort of info I was looking for when I wrote it.