The rough timeline, paint scheme and types of KTs goes like this:
1) Porsche KT - First 50, curved front, most used 18 tooth sprockets with Gg 24/800/300 multi-link tracks, with holes in the connecting links. All had zimmerit. Camo scheme was soft-edged.
2) Zimmerit Henschel KT - Produced till Sep 1944. Used 9 tooth sprocket Gg 26/800/300 multi tank links without holes in connecting links. All had zimmerit. Most of them had the soft edged camo scheme. The very end of the production had hard-edged "ambush" camo scheme. Keep in mind that not all had the dots applied.
3) No-Zimmerit Henschel KT - Sep 1944 onwards, same specs as the above. All used hard-edged camo. Some had the dots, some didn't. My personal opinion is that most didn't have the dots, if you look at wartime photos. For example, KT 332 and 204 are shown with the dots in the camo scheme for Tamiya, but if you look at the actual photos, they didn't have them. Very few did.
3a) Everything same as above, but there are numerous conflicting sources that say oxide red primer was used instead of the standard red-brown due to paint supply issues. Some even say that only dunkelgelb over oxide red primer was used. Some sources say the order was not to paint dunkelgelb all over, then apply the other 2 colours over it, but to just apply the paint in their respective areas to save paint (hence, the tank will look exactly the same as #3) - There are no pictorial evidence of this due to lack of colour, but there are documents with orders, some worded quite strangely, hence some modellers do this colour scheme.
4) "Octopus" KT - No "full" version has ever appeared. There are 4 differences, which I'll list here:
i) They are supposed to have 18 tooth sprockets
ii) They are supposed to have the Kgs 73/800/153 tracks single links
iii) They are supposed to have single link hangers on the turret, and rings on the side to put foilage on. (the older ones hung 8 "sets" of multi tracks, 2 on each column. The newer ones had 12 sets, 3 on each column).
iv) The "Octopus" camo scheme - This is debatable. Many say its a new scheme. Some say its a custom scheme. I personally lean towards a new scheme, as you wouldn't want your tank to stand out and be targeted down. Some say its to represent a last hurrah from the final Kassel factory. The unusual things about this scheme is that its dunkelgelb over a olivgrun base, and of course, the weird octopus rings. Apparently the issue was the Dunkelgelb was running low.
The famous Kassel Octopus KT was an incomplete crossover - It had the new sprocket, but only the smaller railroad tracks, and had the old turret. So, the only thing new about the Kassel KT was the sprocket and camo scheme. By then, the track factory had blew up, so they had to make do with the railroad tracks. They used the old turret with multi-link hangers, which was puzzling, as there were a lot of the newer turrets lying around in the factory (alongside with a lot of the older ones), so they were probably trying to "clear old stock"
Also, the Kassel Octopus had 6 other sister tanks which were given to Pz Abt 510 and 8 to Pz Abt 511. The Kassel Octopus was one the the 8 given to 511, and all were abandoned and destroyed by their own crew. Same for the 6 given to 510 which were abandoned.
The only photos of the Octopus colour scheme was for the single one at Kassel. However, I think its reasonable to assume there would be others in all sorts of combinations of turrets, sprockets, tracks and colour schemes which were used.
References:
https://tanks-encyclopedia.com/ww2/n...onigstiger.php
Technical details
http://histomil.com/viewtopic.php?t=3918&start=4510
https://www.gamereplays.org/companyo...maps_sturzdorf
Tiger I Information Center - Unit Histories