The first thing I did was to make some diagrams, expanding on Escher's creature as well as I could. Escher's published work containing the Curl-up constists of three drawings, Curl-up
, House of Stairs
, and House of Stairs II
. These drawings are of course art, not a drafting diagram, so I had to make up some parts that were never shown clearly. I discovered that Escher cheated, too: the Curl-up's head is, in the standing posture, clearly the widest part of its body, but in the curled-up posture the smaller body segments encompass it, without any apparent stretching or bending. Although, with Escher's theme of realistically drawn but physically impossible objects, this isn't really surprising.
The Curl-up (in most cases I could observe) has a carapace with 18 body segments plus its head, with the last one, the tail, finishing in a rounded point instead of attaching to another segment. There is some inner flesh that protrudes a little from the head shell, but the underside of the body is never shown clearly. There are three pairs of legs, with a quite human knee and foot attached.
I decided not to worry about the soft, squishy interior until I had the carapace working. I numbered the segments starting from the one just behind the head. The legs extend from segments 4, 9, and 14. The join between segments 1-2, 2-3, and 3-4 have a significant reverse bend in them when the Curl-up is standing normally, to keep its head raised. Some of the later segments also have a slighter reverse bend but this depends on the Curl-up's movement and activity.