Okay, I found this resource image...

https://www.deviantart.com/llexandro/art/Sci-Fi-Texture-246-777543120

That I would like apply to a surface, the final effect looking like a full disc.  I would think there's a way to link some nodes in the "Material Room" to create this effect, but I can't solve the formula.  True, I could also do this in an image editor like PaintShop Pro, but the final image would be 8000 by 8000 pixels unless i shrink it and I'd rather not lose the detail.

Any clever "wizards" willing to share the secret?

How do you plan to use the final image? Many ways to shrink image without losing detail. In the example below I did not shrink anything.

I addressed the 2D solution, to me that is the simplest way to do it. 

Neat demonstration.  I presented the same question upon a small private forum I also haunt and while I was away, a friend stitched together the image as you did (just without the "watermark") making my request kinda' pointless.

Still, thank you for taking the effort to demonstrate the 2D approach is the most straightforward solution.

For future reference, here is how you can do it with the traditional Image_Map node. With the Cycles ImageTexture node, one has much more freedom to wrangle the texture coordinates as desired, but on the downside one does indeed have to figure out the formulas oneself.

Ooh, "Cycles"?  I gather that's for Poser 11 or higher?  I should have stated that I am using Poser Pro 2014.  It doesn't have "Cycles".

The Image_Map node that ODF used should work fine with Firefly in Poser Pro 2014.  ODF mentioned the Superfly Image Texture node as being a bit more difficult to use but that's not what the demonstration is.... Hmm.  I'm not sure I made any sense there.  Anyway, the demonstration should work in Poser Pro 2014. =)

Teh Mollz

P.S.  I'll be using it myself! XD

Well, good thing I did not post the version that requires Cycles then. I _think_ the version I showed will work with Poser Pro 2014, but I don’t have anything earlier than Poser 12 installed, so I won’t swear by it.

So, I've figured out how to do fancy texture manipulations with just the traditional material nodes, no newfangled Cycles stuff. Once again, that does not necessarily mean this will work in Poser Pro 2014 because the workings of those nodes may have been changed in the meantime. But at least there's a chance...

(Kaleidofemme, lol!)

Is it weird that Antonia is wearing La Femme 2 as a dress pattern?

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Heh.  Hilarious! XD

Teh Mollz

Kaleidofemme makes me happy, and I don't know why. :D

Just so everyone knows, odf's kaleidoscope works in Poser 6 - the earliest version I have available which has Firefly.

I'd also like it to be known that I have no intention of reinstalling Poser 5 just for the sake of this. I'll leave that to some other obsessive. :)

Edited to correct the screenshot image - which was semi-transparent for some reason which I'm trying hard to resist investigating...