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Origami Halibut




The biggest kind of flat fish, which is a group of fishes whose eyes are located on one side of its body. They lie on the sea floor with "eyed side" on top, camouflaged among the sands, and look around to ambush prey.

Design

I have an idea for flat fish since 2021. The catalyst was my poison dart frog design. When I folded its eyes, I noticed how they form 3D bulges and the color changed interior are facing opposite direction.
My poison dart frog from 2021

This reminded me of flat fish. Most flat fish origami out there has a flat color changed eyes, like the one from Hitoshi Kakami, Inayoshi Hidehisa, and Tu Kaiming. Adding the flat fish roster with this slight variation would be great. So the design began.

Excluding the eyes, I gathered these essential features to be expressed:
  1. Big gaping mouth, or at least pronounced lips. Fish origamis are great when their mouth are gaping open. My favorite is this epic tarpon by Takuorigami.
  2. Seamless body. It is attractive to have that wide body free from lines.
Fish origami is actually hard to design. They have many wide surface area and the common technique of uniaxial circle and river packing that I usually use is not good at it. Free folding should yield better result, if I can pull it off.

Later that year I free folded this out of chocolate wrapping paper. I successfully got the mouth as planned but adding eyes would be difficult. There was no more progress as I favored other ongoing design. This design was forgotten.



When I participated in the East Bay Origami Convention 2023, there was a fun session called "giant origami" or something. You were given huge paper (about 1 m) to fold anything. Since I have always thought it is cool for anglers to pose with their big fish, I figured out that huge fish model would suit this activity. I skipped that to catch the train, but it sparked my interest to continue designing flat fish. The species would be halibut, since it is the largest kind.

In preparation for future similar activity, I added one more design goal: high efficiency. Meaning that the ratio of folded model compared to initial paper size is high. To make high efficiency possible, it is okay to have the eyeless side of the fish "messy". The model will be optimized to be looked at from one side.

I prototyped this flat fish by free folding. Like the poison dart frog, the eyes of this prototype are folded out of 22.5 degree corner flap. It can be spread open to make it 3D. Making the dorsal (top), anal (bottom), and caudal (tail) fin is easy. Just bunch of pleats and crimps here and there. The hard part is pectoral and pelvic fin. Pectoral fin, or the fin behind gill cover, needs to be sufficiently long. It is hard because of its location; sprouting from the middle of the paper. This prototype has limitation in representing it.


Based on preliminary base.

I spent any idle time by free folding. The idea is eyes should be made of corner, and pectoral fin is made of middle flap. Then the mouth can come from edge flap Something like this:

Weeks passed, no advancement. I couldn't make the pectoral fin sufficiently long, and work out the mouth shaping.
... what am I?

I decided to ditch the idea that pectoral fin should be made from middle flap and reassign it to be an edge flap. There is a straightforward structure for that layout:

This structure doesn't satisfy the requirement of seamless body. Luckily we can do some swivel maneuvers to shift the tiny flap to be just behind the bird base's middle flap.

The corner flap will be made into eyes. Let's draw it in the crease pattern.
This structure is similar with poison dart frog's eyes

One edge flap can be folded down to make pectoral fin. However it can't reach its maximum length potential. There is a locked paper that prevent it to be pulled all the way to the back.
Attempting to inside reverse fold the thin flap will result in obstruction by starred internal corner.
Self intersection will occur if we force to fold it up. The yellow region shows the starred corner from previous picture.

That locked paper can be removed by sinking it to the back (or unsink it, depending how you look at it). I found one way to sink it on paper which looks somewhat cool, but it is very difficult to fold. No idea how I found it in the first place. It was a combination of mush and forced squash and I don't want to do it again.

Luckily there is another solution. Easier to fold, but still hard to do since the sink has to be done from inside. A better way is to crease through the layers, unfold everything, and reassemble it correctly.
Sunken internal corner

Inside reverse all the way in, successful

For the mouth, I realized we can do a massive valley fold down from behind. This aligned the edge flap with the model's head, and the pointy flap can be folded up to form lower jaw. 

I free folded the tail with pleats and saw the potential to use the top and bottom edges as dorsal and anal fin. The body was not long enough so I changed the reference to be based on silver rectangle. This also provides more paper for those fins.
Silver rectangle's ratio is \(1 : \sqrt{2}\)

There is one more fin: pelvic. Turning around the model, we can see some raw corners. By free folding using the existing creases, I swiveled it to the front and form a pointy end. Only after drawing the CP I found a sequential way to fold it.

I made a lot of test folds to alter the shaping. The final result minimized the amount of layers on upper jaw, and made the lower jaw flap able to hold the upper jaw corner. On paper of at least 25 cm, the paper should be able to hold its position. By the way the efficiency is about 74%.
With Inayoshi Hidehisa's bastard halibut.

It is worth to notice that the tail shaping part will eventually produce non 22.5 degree creases. We can change the silver rectangle reference to something else to make it truly based on 22.5. However the folding process to locate that reference is quite tedious so I just leave it with silver rectangle.
The reference on the right is based on \(13 + 8\sqrt{2}\)

Halibut's eyes are actually on its right side, and I have been folding them on the left side. The crease pattern has to be mirrored to reflect this asymmetry. If you came here from Instagram, please use the crease pattern on top of this page. This error happened because of my habit of drawing CP from left to right.

Paper Preparation

To be trendy like the Japanese pro folders, I've got to step up the paper game. I can use a brown tissue with white tissue underneath, and apply some white droplets on the brown side. I learned a technique from high school art class to fling tiny droplet of paint with brush and stick. You first dip the brush tip to the paint (don't let it soak), then use a stick to stroke the brush tip. When the brush's bristle return to its position, droplets of paint will be flung. Control the paint droplet projectile by changing the angle of the brush and your stroke.
!!! PLEASE WEAR EYE PROTECTION !!!

The benefit of this technique is the droplet will be tiny, much smaller than a normal droplet from things like eye drop. You might see the same effect if you don't close your lips while brushing teeth; the tiny toothpaste droplet will fling alll around you.

I tried it on double tissue and it looks pretty decent. Be sure to cover the unused treating surface with scrap paper to prevent the droplet to spread all around it as they are hard to clean.

Fold

Folding is easy, but the final result has something off. I realized that there are too many white spots and they obscured the details near the head. It is especially difficult to differentiate the white color from the spot vs the color changed eyes. I ditched this fold and make a new paper from tissue + wenzhou to better make the color changed eyes more contrast, and water down the acrylic paint.
The first "final fold" with cloudy eyes

Finally it's done. I am happy with the result. This is a somewhat intermediate model that can be taught at convention. To celebrate, I had a halibut dinner.

Halibut dinner for the next day


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