Compiled notes and images......
SCARF VERSION ONE - Seasons 12/13
12 - The scarf started off at thirteen and a half feel long when it was introduced during season twelve. This was however a little too unwieldy, and in between filming the Sontaran Experience and the Ark in Space (Ark was recorded 3rd, broadcasts 2nd) a section of blue grey was removed, on the side with the camel and purple stripes at the end. During the Ark in Space the scarf gets blasted by a security system which leaves a small hole in the purple beige end of the scarf. The scarf then remained unchanged for the remainder of the
12.5 - Identical to 12 except that a large grey stripe is missing. And he got a hole in the end of it.
13 - (Looks just like 12 only a few rows are truncated off one end)
The scarf was trimmed again at the beginning of season thirteen to a mere twelve foot. The other end got the whole bottom section removed so the scarf ends on Gray, Red and Yellow. When combined with the previous alteration, the scarf has lost about 18 inches since it stretched out. The “stunt” scarf is seen for the first time in Android Invasion when the Doctor and the double are fighting. The scarf stayed in this format for the rest of season thirteen.
SCARF VERSION TWO - Season 14 (A lot like 12, but shorter)
14 - The original scarf goes under two more alterations before the season films. Both ends are shortened, the camel and purple stripes are removed on one, and the red and yellow removed on the other. There were actually two used during filming: one was ten and a half feet long, while the other was only ten feet long. In most of the episodes of this season the shorter scarf is used for indoor filming, while the longer one is used on outdoor shoots, The Mask of Mandragora, The Hand of Fear, and Deadly Assassin. (There is one anomaly; the scarves are swapped around in the Hand of Fear.)
The trick is to look at the ends of the scarf in indoor shoots and outdoor locations. The “stunt” scarf did not have alterations made to it, so it still has the bottom stripes from Season 13. After DA, the “stunt” scarf was used exclusively.
SCARF VERSION THREE - Season 15 (This one has the true green in it, and light blues)
15 - There is one longer version of the Dr Who scarf, a whopping seventeen foot scarf. This is used in three
of the episodes; Image of the Fendahl, Underworld and Invasion of Time. Strangely enough, this Dr
Who scarf design had the shortest time on screen of any of the scarves.
The BBC did release the design for the Dr Who scarf, however, the version of the scarf they produced
was actually the third and not the original version. http://www.androgums.org/scarf.html
SCARF VERSION FOUR - Seasons 16/17/18
16 (This one has grey in it)
In the final two seasons of the multicolored Dr Who scarf, it was quite severely adapted. This scarf was a
combination of two previously used scarves. The original scarf and “stunt” scarf are joined, with the original being alterated two more times, with two sections removed close to the neck area. Thus the 20 footer was born out of the old scarves.
The 20 footer remains the same until Shada, where a section of the original scarf (the section that used to wrap around Tom’s next when it was longer) is moved down to the end of that part of the scarf and everything is reattached. Then one of Tom’s vests (probably the “stunt” vest used in Android Invasion since it was shot up) was used to make patches for the scarf.
(Ok technically this makes FIVE scarves, but I'm only counting the multi-color ones here)
The multi-color scarf was finally replaced in the fourth Doctors final season, season eighteen, with a burgundy monochrome striped scarf. This burgundy scarf started off at around twenty feet, but stretched to a memorable twenty four feet during the season.
Over the season it stretched out so much that by Logopolis, Tom had to wrap it around twice. It also became very damaged. It had so many holes, rips, and frayed edges that JN-T (stated in an old DWM interview somewhere) had it ripped up in Castrovalva.
Info found at http://purpleblancmange.wordpress.com/2011/02/16/my-first-visit-to-the-bbc-1991-to-1993-updated/#comment-925
and at http://api.ning.com/files/Tsax2hh5*KeIYSt-W7Z9jHc2NdZOET9RH-0fOIhN8wJXoBlZUtw3VvBcE*ZMDKj2galVpL84WbM2Whs5gywUQ8dxZcXt13aa/DrWhoScarfHistory.pdf
and of course this can also be found at http://www.doctorwhoscarf.com/history.html