Koi, by Robert Lang, with some adjustments by me.

This is a model from Origami Design Secrets–actually, it’s on the cover of the book.  It is a demonstration of the technique of pattern grafting, where you fold a flat pattern into the paper before going on to fold the general shape.

Robert Lang’s design is well and good, but I have a tendency to work with 15 cm paper at largest.  It’s not ideal for a lot of types of models, but it is my self-imposed constraint.  So, in my version, I made the scales very large relative to the size of the paper.  In Lang’s version, the scales are one quarter the size in both directions, meaning there are 16 times as many scales.  Lang’s version is more realistic, while mine mostly just evokes the idea of scales.

So the funny story was, I was thinking about how I could adjust the model to work with 15 cm paper, and I woke up one night thinking, “Of course!  I should just fold the paper into a 29×29 grid!  Then the proportions can remain the same and all the math works out!”  It turns out that my dream math isn’t very good, and 29×29 makes very little sense.  But it worked out anyway.