In goldfish terminology, "fancy" means double-tailed. They were first documented in the Ming Dynasty (C.E. 1368-1644) of China. From an evolution perspective, such mutation is detrimental as it makes them incapable of swimming faster and thus less competitive for natural selection. Goldfish breeders, however, do love such appearance, and various breeds has been kept ever since due to articifial selection. This design of mine was roughly based on a certain breed like the one show in the next picture.

This model was my first fish design and an example of applying my early knowledge of ERM to the 22.5° system. I still kept my old note back then, which contains my hand-drawn abstraction and the ERM map for this design, as shown below. One may compare the map with the actual map shown later and see how much they resemble each other. (In the sketch I only put one anal fin; I later realize that fancy goldfish actually have two anal fins as well, so I fixed it in the final version.)

One of the major difficulties with fish designs is that the dorsal fin tends to consume a large area due to the additional rivers in its front and rear side. This typically will cause the lakes corresponding to the body to separate far apart at least on one side, leaving huge space there that is difficult to justify. However, the doubled tail of this subject cleverly justifies the space on the rear, and it also leads to a symmetric layout that is easier to fold.

這篇文章 Fancy Goldfish (Carassius auratus), 2016 最早出現於 Tsai Origami。

This design wasn't exactly based on particular species of Cockatoo, but it more or less resembles the sulphur-crested cockatoo, yellow-crested cockatoo, or the Major Mitchell's cockatoo (without the color changing effect). To be honest, I didn't thoroughly study cockatoo species and anatomy before I work on this design, so I made several mistakes on my first version. It was Robert J. Lang who pointed out those mistakes and drove me into fixing them as much as I can.

There are still some anatomical imperfections about this final version, but from a design perspective, it's not a bad design at all. It has a fully closed 3D body, a 3D head, and a very efficient ERM-inspired layout. The idea of allocating the crests as middle flaps may sound crazy, but it turned out that doing so nicely balanced the outflow and also results in a very interesting folding sequence.

However, as mentioned, there's still room for improvement. Arguably the biggest issue is that I didn't make the color change at the crests and the layer distribution made it look like the crests are coming out from the back of the head (whereas they really all come from the front). Another structural issue is that I used a bird base to create the claws since I initially believe that cockatoos, like most birds, have a 3-to-1 claw formation, but only later did I learn that they actually have a 2-to-2 formation, and it's much harder to shape a bird base nicely into that formation. I would certainly do these differently should I revise this design.

這篇文章 Cockatoo (family Cacatuidae), 2017 最早出現於 Tsai Origami。

This model means a lot to me, as it was my first design that takes more than 100 steps to fold, and it was also the very first design I sent to Robert J. Lang in our correspondence. I still remember how he enjoyed folding this model, and how his words of encouragement drove me into origami pursuit ever since.

There are many elephant designs of this level of complexity, and my goal in designing this model was to achieve theoretically optimal efficiency. I studied various elephant designs (especially those listed in Lang's Origami Design Secrets) and try to understand why some of them are less efficient than others. Since most elephant designs are not uniaxial, tree theory couldn't quite help me explain the source of inefficiency, but my own theory of ERM (which was still in its infancy by then) generalizes the idea of tree theory, and I came up with a technique called "outflow analysis" that enables me to diagnose sources of inefficiency in non-uniaxial designs as well.

Perhaps the most surprising conclusion of outflow analysis is that large pieces of land, even continents, are not necessarily causing inefficiency. The only two things that matter are:

1. The outflow, which is defined as the total width of the rivers flown to the sea.
2. The total length of the coastline, which is where the lands touch the sea.

Once both these are minizied, it doesn't matter how much land we still have in our ERM map, and the design is actually theoretically optimal (with respect to the given abstraction).

In the figure above we can see a rough ERM map of my elephant design. Although there are quite some lands near the shoulders of the model, this design is essentially optimal as it minimizes both the outflow and the coastline (only the necessary peninsulas contribute to the coastline). As a result, among all the elephant designs of the same level of features and details, mine is noticably larger than the rest if folded from the same sheet size.

這篇文章 African Elephant (Loxodonta africana), 2016 最早出現於 Tsai Origami。