Is there any info about how the paintings function? [duplicate]

Question

So in both the books and the films Dumbledore's (headmaster's) office is filled with the paintings of previous headmasters. Even if the person the painting is of is dead they are still there and able to respond.

Do we know whether the paintings can think for themselves and learn and grow in wisdom? - although the fact they can learn or at least remember is demonstrated frequently.

Do they answer with all the knowledge of, let's say, Dumbledore would?

In my mind it's akin to being a ghost, or I guess even a horcrux of sorts. Leave behind some soul within a painting?

Answer 1

According to rems answer to this question, J.K. Rowling already answered.

Q: All the paintings we have seen at Hogwarts are of dead people. They seem to be living through their portraits. How is this so? If there was a painting of Harry’s parents, would he be able to obtain advice from them?

JKR: That is a very good question. They are all of dead people; they are not as fully realised as ghosts, as you have probably noticed. The place where you see them really talk is in Dumbledore’s office, primarily; the idea is that the previous headmasters and headmistresses leave behind a faint imprint of themselves. They leave their aura, almost, in the office and they can give some counsel to the present occupant, but it is not like being a ghost. They repeat catchphrases, almost. The portrait of Sirius’ mother is not a very 3D personality; she is not very fully realised. She repeats catchphrases that she had when she was alive. If Harry had a portrait of his parents it would not help him a great deal. If he could meet them as ghosts, that would be a much more meaningful interaction, but as Nick explained at the end of Phoenix—I am straying into dangerous territory, but I think you probably know what he explained—there are some people who would not come back as ghosts because they are unafraid, or less afraid, of death.

source from Accio quote, Edinburgh Book Festival, 2004

To sum up, let's say that paintings are like memories. People on paintings can only "repeat catchphrases", because they leave a part of their aura behind them, and only in places that were highly related to them. So yes, in a way, they leave something that could be assimilated to "a part of their souls", but that's all. They can give some advice, but nothing that you can't remember or expect from them.

Answer 2

If I remember correctly, they couldn't really think for themselves. What they did/said depended on what they used to be while they were alive.

Here is what I found on the Wikia:

The subject of a magical portrait is sentient due to enchantments placed on the portrait by the painter. The portrait will be able to use some of the subject's favorite phrases and imitate their general demeanor based on how the subject appears to the painter; however, they are limited in what they can say or do.

So, the portrait of Dumbledore wouldn't answer with all the wisdom of his, but it would be able to imitate him and his behavior.

Also, there were some paintings in Hogwarts that pictured people that were not headmasters.

Here are some Known Portraits.