These are knee socks made on a half-scale version of the pattern for the Fourth Doctor’s scarf from Season 12 at doctorwhoscarf.com . Specifics follow:
TOE
4 purple (cast on)
20 tan (increase on odds; finish with a non-increase plain row)
toe=24
FOOT (stockinette on sole; garter on top - knit odds, purl evens)
6 tan
8 brown
5 (4) yellow
11 (10) red
4 purple
22 gray
11 (10) green
4 yellow
15 (14) tan
8 red
4 brown
6 purple
foot=100;
sock=124
HEEL (short rows)
11 (10) green
5 (4) yellow
9 (8) gray
5 (4) red
26 tan
4 purple
heel=56
sock=180
LEG
11 (10) green (pick up + twist two on each side in 1st row; keep twisting those stitches; decrease the picked up stitches in 3rd 4th rows)
7 (6) gray
4 yellow
10 red
4 purple
20 brown
6 tan
4 gray
21 (20) red
8 yellow
11 (10) green
4 purple
22 tan
6 brown
11 (10) gray
4 red
7 (6) purple
4 tan
8 yellow
28 green
8 red
7 (6) gray
5 (4) yellow
10 brown
5 (4) purple
6 tan
18 gray
4 red
7 (6) yellow
8 tan
4 purple
16 brown
4 red
leg=292
sock=472
CUFF
18 purple
sock=490
Starting from the toe: I cast on 12 and increased to 64. The toe is stockinette. The foot, like the “pattern” says, is garter on top and stockinette on the bottom. On the short-row heel I left only four stitches unwrapped, so the heel is a little pointy, but it will round out with wear. The first green stripe after the heel, I maintained the foot pattern of garter on the front and stockinette on the back for the first six rows; for the last four rows of that stripe, I switched to garter all the way around, and the leg is garter all the way up to the cuff, which is 1x1 rib.
The numbers in parentheses are the numbers of rows I actually did on those stripes. The sock is a half-scale scarf pattern, like I said, and where halving the row counts gave me an odd number I rounded down to keep the color changes invisible (because after all, socks, unlike scarves, have an inside). I used Brown Sheep Nature Spun in fingering weight and size 1 (US) needles, and I get 9 st/13 rows/inch in stockinette. The foot fits a size 9 1/2 foot and would probably stretch to fit size 10 if you didn’t want to make changes. The leg doesn’t really fit all the way around my calf, but my calves are on the sturdy/athletic side; Ellen’s legs are skinnier and the socks fit her fine, but take that into account if you’re making some for yourself. At this gauge, you want the legs going in the socks to be about 12” around at the widest point, is my guess. (Mine are 15”, and no dice. The model picture with only one leg in it is of another friend whose legs are in between Ellen’s and mine w/r/t calf circumference, and they fit her okay, so use your judgement.)