In Ship in a Bottle, the crew of the Enterprise tried to give Moriarty the ability to leave the holodeck. They tried beaming out a chair but it didn't work. In the episode with the Exocoms, they established that they make holograms of devices that actually work. Well, what about a holographic hologram generator. That is, a hologram generator that is also a hologram. Would this work? What about using the hologram generator to generate its own hologram in addition to another holographic object? Then they could, say, give the Doctor the ability to leave the holodeck without his mobile emitter.
A hologrid has elements in all 3 dimensions, up-down, left-right, and forward-backward or the XYZ axes. This is necessary to generate a 3D hologram and project the force fields everywhere in the holodeck. They have stated that the holdeck is a trick of photons and force fields. A holodeck is not capable of creating another holodeck, just a simulation within a simultion. They actually had to remove the holomatrix running Moriarty's program and keep it running to fool him, as they were totally stymied in everything else they tried. The Exocomps had an actual replicator on their "nose" that could replicate the tools that were necessary to perform specific tasks.
Yes, the Exocomps are not a good argument in this context. But the Krieger wave generator from TNG "A Matter of Perspective" is. This highly complex device was created by the holodeck, and appeared fully functional, not only in the context of the simulation, but in terms of interaction with the real world as well. A holographic hologram generator thus sounds perfectly possible. However, a holographic hologram generator would need to be created by a hologram generator... So either you need at least one "real" generator somewhere down the line, or then you have to have holographic holo-generator A generating holographic holo-generator B, which in turn generates A. And this sort of a perpetual motion machine sounds, while not impossible, at least extremely complicated. Where does the power come from? How to prevent disastrous positive feedback where a minor disruption in the way A generates B will cause a disruption in how B generates A, further disrupting A's efforts? Timo Saloniemi
I see what you mean. The Krieger wave generator is indeed a better example. It really isn't a perpetual motion machine because no energy is being created. A holographic hologram generator would need a holographic battery, of course! You might need a physical memory apparatus, but that can be relatively small as seen in Ship in a Bottle. The way to build one is quite easy. Start by simulating the machine in a holodeck. Then have the generator overlay forcefields over top of the holodeck's forcefields. Then turn off the holodeck's forcefields. What remains is the holographic device's forcefields. There could be a problem because the hologram machine needs memory for not only itself but whatever extra hologram it makes. Worse case scenario is that the memory cells might only have enough memory to project themselves (tho there should be ways around that using recursion, etc). However, using physical memory cells in a small package was already established, so an "almost completely holographic hologram generator" should be possible.