Let's try to understand the reasons and meaning of this behavior of cats.
What factors influence the fact that a cat stamps its paws and purrs, how is this connected with its instincts and emotions?
How to correctly interpret and respond to this gesture, and what problems can it cause?

Shows affection
Cats have many ways to show their affection for humans, but kneading and purring are among the most commonly used.
By kneading and purring, a cat is claiming a person as its own (and perhaps also marking them as a member of its family).
Wants attention
If a cat comes up to a person sitting at a computer and distracts them by purring, it most likely wants to be noticed. It will do this if the person has always stopped what they were doing and petted it.
Relaxed and happy
Kneading and purring may also simply indicate that the cat is relaxed.
The pet will also blink frequently and slowly, purr and look incredibly sleepy.
In fact, the cat may end up just falling asleep right where it sits within a few minutes.
Instinct
Probably the most important reason why a cat kneads and purrs is simple instinct.
Kittens who are nursed learn to knead the mother cat to stimulate milk production, and the association with food reward following this action is a positive one that tends to persist throughout their lives.
This means that even as a cat gets older, it will often continue to knead with its paws because it reminds it of comfort.
Makes a good sleeping place
Sometimes cats knead and purr because they are making themselves a cozy bed. It is similar to how people fluff up their pillows before they lie down on them.
If you see your cat kneading the blanket with its paws, there is a good chance that it is getting ready for a nap.
Stress
A cat may also knead a person or object with its paws to calm itself down when stressed or anxious.
If this is the case, she will most likely not fall asleep during the massage (or immediately after). You may also notice that the pet's tail is twitching or pressed against the body, the pupils are dilated, or the ears are pressed.
If you think your cat is stressed, there are ways to help reduce it, such as changing the environment or using calming sprays.
Territory marking
Territory is important for a cat, especially if there are several cats in the house.
One way a cat does this is by leaving a scent through one of the many scent glands found on its face and paws.
When a pet starts kneading its paws and purring in a certain place (or on a person’s body), this may mean that it is marking its territory.
Warming up
Cats love to get some exercise every now and then, which is one of the reasons they love scratching posts.
Scratching posts allow your pet to stretch all types of muscles in his back and legs. Sometimes, your cat may use kneading with his paws as a form of stretching.
Estrus
Kneading and purring may indicate that the cat is in heat. She is trying to attract a male cat by lying on her side or back and kneading the air with her paws.
You may also see other signs, such as whining or being more affectionate than usual.
She'll give birth soon
If your cat is pregnant and she is kneading the blanket in the box with her paws, this may be a sign that she is about to give birth.
Pregnant cats often begin to build some sort of nest to prepare for the arrival of their kittens.
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