Punk budgies in Tollcross: the visiting waxwings.
Two winter visitors are particularly worth looking out for: the (frequent) redwings and the (rare) waxwings.
In Dutch, the waxwing is the pestvogel. You can treat both names as clues. Waxwings refers to the little wing feathers that look like drips of wax. And as far as the local thrushes are concerned, waxwings are a major pest. They arrive in huge flocks, their song tinkling like sleigh bells, to descend on parks and strip the rowans and whitebeams of almost every berry available. You'll often see angry mistle thrushes trying to drive them off. It won't work.
Waxwings have a complex, caring social nature, and so the easiest way to find them is to wait by a berry tree and look out for an airborne flock. (A large flock of other small birds, if it lands on the ground, is more likely to be redwings or starlings. Waxwings stay in the air or on the tree. A small group of a few birds may be sparrows.)
Here, they landed on a sycamore near Tollcross and spent about 45 minutes there. They appeared to be eating insects, which they do in the breeding season, but I was a bit surprised to see this in January: their main diet is berries.
Spotting waxwings takes a lot of luck and planning, though. If you're keen on seeing them (and they are beautiful), it's worth tracking their arrival through Twitter, either by following @birdinglothian or @waxwingsUK, or just doing a daily Twitter search for waxwings Edinburgh. It's much easier to spot redwings.
These small thrushes can be seen all over the Meadows during winter, especially anywhere on the ground where there are heaps of leaves. A good spot is near the croquet club and across the road in the Tollcross corner. You'll sometimes see them together with starlings, in search of the worms they both like to eat.
These confident little birds are fairly easy to get near, if you take your time approaching slowly. As you can see from the pic below, they can be nearly invisible among the leaves, and only easy to spot when they move: which luckily they never stop doing for more than a few seconds.
Close up, look for the eyebrow and the red patch under the wing.