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As I understand it, a hologram is photons projected onto complex forcefields. It could be anything, from a bald humanoid to a Teenage Mutant Ninja Turtle doll.
The holo-matrix is the software that runs the program. Doc's is extremely sophisticated since it contains more than a preprogrammed responces, but also personality and adaptive elements. The holo-emitters are independant pieces of hardware which are controlled, along with the holo-matrix, by the ship's computer.
------------------ "A gathering of Angels appeared above my head. They sang to me this song of hope, and this is what they said..." -Styx
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But nowadays every other hologram is senient and considered a living person...made up of photons and forcefields.
------------------ "Everyone should speak English or just shut up, that's what I say!" - Calvin. This post is sponsored in part by the Federation Starship Datalink
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Well, it's not so much that the computer is a sentient being, it's the program running on the computer that is sentient.
Like if Photoshop suddenly started typing things on its own and creating pictures of me getting killed to try and get me to stop scanning in Star Trek pictures. That doesn't necessarily mean that my Dell is intelligent, just Photoshop.
------------------ "A gathering of Angels appeared above my head. They sang to me this song of hope, and this is what they said..." -Styx