This Doctor Who scarf is not meant to imitate any of the particular reincarnations of the Doctor's wardrobe, but to capture the essence of random color and long scarfiness.
Cast on 50 stitches on #10 (6 mm) needles.
Row 1: Work 1x ribbing (k1, p1)
Row 2: repeat row 1 until long enough to suit you
These color changes are pretty much random.
I tried to alternate between warm and cool colors, but not always.
I tried to keep the number or rows per strip between 3 and 15, but not always.
You can choose to slip the first or last stitch for a neater edge, if you like.
Your Doctor Who scarf should be as random as your bag of leftover yarn :-}