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Due to changes in Bryce 3D, the original rainbow tutorial will not work. This tutorial shows how the new rainbow settings work.
Pick Carribean Clear as the Sky preset. (You can use any sky, but Carribean clear makes it very easy to see what is going on.)
Click on the Sky and Fog title. (Not the drop down arrow to the right of it, click on the Sky and Fog title itself.)
Click on the cloud/rainbow icon that shows up.
Go to the Atmosphere tab.
Enable the Rainbow and set the Opacity to 100. (Again, this is for ease of use. Often you'll want a lower setting for realism.)
Go to the Sun Settings. Click on the number next to Azimuth and change it to 180. Change the Altitude to 20.
If you look at the preview screen, you'll be able to see the tips of the rainbow.
Radius - that affects how thick the rainbow is. The larger the radius, the wider the rainbow is.
Opacity - how bright the rainbow is. The higher the number, the clearer it is.
Secondary Bow - some rainbows have a double bow. This activates it.
Link Sun to View - this means that no matter where you point the camera, the rainbow will show in the same position. This is great for static scenes because you won't need to adjust the rainbow settings if you move your camera, but it doesn't work well for animation because the rainbow shouldn't remain static if the scenery moves.
Azimuth - This controls the sun's horizontal position in the sky, and thus affects the rainbow. If you Link Sun to View and set the azimuth to 180, then the rainbow will be perfectly centered in your scene horizontally. If you don't link the sun to the view, then you'll have to play around with this setting so it is correct for your scene.
Altitude - This controls the vertical position of the rainbow. 20 is about the minimum setting to see the rainbow if you have it perfectly centered while 42 is about the maximum before it disappears into the horizon. (If you shift the rainbow so you only see one end, then the lower the Altitude, the steeper the rainbow curve while the higher the number, the rounder it is.)
Well, I hope this takes some of the mystery out of the new, improved Bryce 3D rainbows.