It's.. a background that takes the place of the lowest layer's transparent color (pink in the RTP sets). In other words, any pink that's on the lower layer will be replaced by whatever background you select. If there's no panorama selected, it'll default to black within the game.
(Thanks Chruser for the image hosting. www.picaroni.com)
Nothing too difficult here. Parallax backgrounds are taken from the Panorama folder. They're 640x480 as usual (in RM2k3) and 256 colors. You can set the picture to automatically move when you do, but slower (for a more background-y effect) or automatically (for clouds and such).
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Remember, when you import graphics, you click on the color you want to be transparent. This works for tilesets as well - that's where the panorama pictures show up.
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Maybe I should define "parallax" while I'm at it - in this case, it's a background that's moving at a different speed/direction than the foreground. That's why RM2k3 calls it that in the Map Properties, yet calls the pictures themselves panoramas.