Design Notes 1: The Cockatrice

What I Want

The cockatrice is one such animal; it's a mythical creature which supposedly results when a rooster's egg is hatched by a snake or a toad. It's normally described as a rooster with the tail of a serpent. The cockatrice is one dangerous beastie indeed; it has the ability to turn its enemies into stone with a single glance.

Anyway, the structure of this fellow is relatively simple, consisting only of a head, a pair of wings, a pair of legs and a tail. As always, it's the details of a model that make or break it. Listed below are therefore the design goals for this model:

1. The head of the cockatrice is that of a rooster and should be recognizable as such. It should therefore have a short beak (two, preferably), and a distinctive comb.
2. The tail should be long and narrow with a barb at the end.
3. The feet should have claws.
4. Bat shaped wings.

These design goals lead to the following choice of constraints:

1. The head must come from one corner of the square. This constraint allows a preliminary base to be added at that corner later on, providing enough paper to form a detailed head.
2. The tail should be as long as possible, so given the first constrain, the natural place to put this would be at the opposite end of the diagonal from the head.
3. Since the tail needs to be long, the wings and legs must be placed in the triangular half of the paper where the head is. Since I'm not too concerned about the exact proportions at this point (who knows the exact proportions of a cockatrice, anyway?), I've chosen the other two corners of the squares for the legs and feet. Preliminary bases can be added later here, which allows greater leeway for the design of the claws, instead of having to rely solely on a standard three point split. Having three preliminary bases at three corners of the square means that there must be a fourth preliminary base at the fourth corner. This is an added bonus that allows the barbed tail to be formed easily, instead of having to spread the point later on.
4. The wings can be formed either from the edge of the paper or from the interior. For simplicity, I've picked points at the edge, of which there are two easily locatable ones - the first is halfway between the head node and the leg node, the second is closer to the head node, located by kite folding the square, with the narrow end at the tail node. Again, since I want a narrow tail, the second choice would be the "logical" choice.

The above constraints lead to a placement of points like this:

Fig 1: Point arrangement

Getting Down to It

Fig 2: Dividing the square

Now add petal fold lines for the legs and head:

Fig 3: Defining the legs and head

A few more lines, at the standard angles, to finish off the crease pattern at the wing regions:

Fig 4: Defining the wings

Now that there's a basic crease pattern, the next question is, does this crease pattern collapse nicely (particularly where the different regions meet)? There's theorems and such out there that can determine if it can, but I prefer the experimental method, so at this point, it's just a matter of pushing and pulling at the paper until something works.

Of course, this process becomes much less painful if you can identify certain bases in the crease pattern. For instance, if I were to kite-fold the tail, and then fold the legs, I notice that the white region of the paper forms a smaller square, with a (semi-complete) bird base within it:

Fig 5: Look, it's almost a square!

The natural step now would be to rabbit ear the tail in an attempt to "hide" it from the square:

. Fig 6: The reduced square

Now that there's a square with just a small bit sticking out, and some bird base creases on it, the obvious thing to do next would be to form a bird base:

Fig 7: Folding into a bird base

It's not quite there yet - the head, wings and feet aren't in their "correct" positions.

Fig 8: Partial base

After a bit of fiddling (just stretching out the bird base, really) I ended up with a satisfactory base:

Fig 9: The completed base

The tail is still too fat, but a few pleats and sinks should take care of that. All that's left to do now is to incorporate the preliminary folds for the head and the legs, make minor adjustments to the flap positions, and add various details:
Fig 10: A cockatrice

So What's Next?

Fig 11: A basic bird of paradise

Fig 12: A detailed bird of paradise

2. Pheasant: fold the tail up and then narrow it.
3. Peacock: fold the tail up even more, and then spread it.
4. Rooster: Pleat the tail to form multiple nested points.
5. Wyvern: Narrow the tail, and add a horned head.

It's also possible to fold dinosaurs from this base, but the tail usually ends up being too long. The tail can be shortened by folding part of it into the model, but that would be a waste of paper. A better way would be to move the leg and tail nodes further back towards the tail node, and then work out a possible crease pattern.

Another possible variant would be to add two more nodes to the tail half of the square, so that the node layout is symmetric about both diagonals. In this case, it takes a bit more fiddling to collapse the base nicely. The result would be a base with a head and tail flap, and then three flaps on each side. Such a base would be suitable for any number of four-legged winged creatures (eg dragon, griffin, pegasus), humanoid winged figures, and six-legged bugs. Fig 13: A basic dragon