Memory foam is one of the latest creations to cater to our creature comforts. It is very solid and dense, and has elastic properties which allow it to recover its original shape over a period of time. It will yield to the shame of your body when you lie down on it, but will return to its original shape when you get up.
In this video you can see what happens when an ordinary Turkish cat encounters such a mattress: it's certainly more bizarre than any of the rugs at the bazaar!