I went out and took some photos with this thread in mind this morning:
Here is a simple example of rebloom: You can see the expired scape, you can see a scape with the buds and you can see a new emerging scape.
'Blonde Is Beautiful'"
Here is an example of what is called bud building on a known budbuilder:
Crimson Pirate:
You can see the spiral pattern up the scape, at the tip of the scape you can see the bloom, and right below the bloom you can see the next bud sometimes two getting ready to replace the last flower when it falls away.Not the best example of the spiral pattern, but you can detect it, often it is much more pronounced that this example.
This plant had a very early scape (the pre bloom scape mentioned above) it looked like it was growing out of the ground next to the plant. Then it produced a crop of rebloom scapes (you can see the dying scapes) now it is blooming on a second set of rebloom scapes, and you can see the a new scape developing down in the foliage.
'Ming Porcelain':