This is probably my most sophisticated design (at publication date) from a structural standpoint. I began by creating the head through doodling with paper. I knew that I wanted color changes on the beak and the cheek spots. The beak would be a flap from the middle of the paper, and the cheek spots would be from the edges.
My first prototype used book symmetry (this line of symmetry can be found by folding adjacent corners to each other, as opposed to diagonal symmetry which can be found by folding opposite corners to each other). The issues were several. The model was highly inefficient, with the head taking up the whole top edge of the paper, leaving very little paper for a body. Secondly the paper build-up was significant, making the head rather thick. I immediately had the thought to use diagonal symmetry instead. The advantage being that 22.5 degree modules can be treated as tiles and easily shrunk along a diagonal axis, with all the edge flaps remaining on the edge.
This was quite straight-forward. I had a prototype in my hands within minutes. The next step was more arduous. I had to find a way to place the creases of the head on a larger square and add creases to get the paper to fold flat. I started by choosing how large I wanted the head to be relative to the larger square.
The reference I chose (shown in turquoise) is commonly referred to as a Kamiya reference (after the eminent Japanese designer who popularized it). I then extended the lines in the head as far as they could go, to create a net of 22.5 degree creases.*
After adding a few more lines to the net so that not all of the creases end up at the edge….
I then have enough lines to create a flat-foldable crease pattern.
The next challenge was to add wing detail, legs and a tail. My first thought was to place the tail (the longest flap) on the corner opposite the head, the legs somewhere on the edges adjacent to that corner, and make the wing detail from the remaining corners.
This seemed to have not left me enough space for legs, and besides, the points of the wing detail were too close to the seam at the belly, and didn’t lie on the back as the tips of the folded wings of a real cockatiel do.
Alright. Wrong direction. A moment of stagnation.
Then it suddenly hit me. Why make things complicated for myself? Simplicity is best. I could use a similar flap arrangement and shaping method to what I had used in my pheasant design. I removed the Kamiya reference, and fitted the inner corner of the head at the center-point of the square. It was simple enough to use the same creases I had from before to make the paper lie flat.
The next thing was to get back the fish-base arrangements of flaps, shown in turquoise. That wasn’t hard, but looks unusual on the crease pattern.
At this point I was done with any work on the crease pattern, and just needed to refine the shaping of the model. (Which was the most enjoyable part.)
*This method of creating nets is also touched upon by Tetsuya Gotani in the chapter Improvising with 22.5 from his book Origamix. It is also covered by Hideo Komatsu in a series of articles in the Tanteidan Magazines. Admittedly, both of their sections focus more on using the net to orient 22.5 degree molecules. As I needed less flaps for the model, I used the lines of the net themself to make the model lie flat. I am also aware of a number of designers who use this method, though we all use different names for it. I prefer the terms net or web over grid, as the lines tend to run in all directions at a number of angles, and do not create congruent atoms (Meguro Toshiyuki’s term for any region of paper completely bordered by creases).