For those who may be wondering, a "gadget" refers to a localized patch of creases that can be placed in different parts of a crease pattern without affecting the entire structure. They are often added after the rest of the CP is finished and can be used to achieve an array of interesting and and useful effects.
Splitting the Ends of Box Pleated Points
The first step of the diagrams below features a small piece of a CP showing a hinge polygon - a "leg" - that, when folded, comes to a point. Now, let's say that this is going to become an insect leg, and we want to have two "toes" on the end of the leg for added realism. Furthermore, let's say that this leg is part of an otherwise perfect CP that would be a terribly huge amount of work to edit. The diagrams on the below present a solution found in the works of Kota Imai that sacrifices a half-unit of the leg's length for the addition of two, half unit long "toes." I realize that there may be more crease efficient ways to go about this but I particularly appreciate this method's elegance.
Level shifters, as described by Lang in Origami Design Secrets II, are something I have found to be exceptionally useful in my models. One day, while experimenting with different gadgets, I found myself asking the question, "what do I do if I want my level shifter to introduce creases 'higher' than axial+1 creases?" Below are my solutions for both types of level shifters described in Origami Design Secrets (the crease assignments may not be 100% accurate, but still convey the basic structure).
A one unit long flap with a normal level shifter incorporated to introduce axial+2 creases.
The addition of more one unit long flaps allows for greater amounts of shifting to take place. This example introduces axial+4 creases into a CP.
A gadget that can be used on the same flap to introduce axial+3 creases.
This gadget introduces axial+5 creases. This pattern can be exponentially increased with the addition of more one unit long flaps to allow for any number of layers to be shifted.
A normal level shifter incorporated into the straight skeleton of a flap to allow for axial+2 creases.
The gadget can be enlarged to add axial+3 creases to a CP.
Axial+5. The gadget can be infinitely enlarged (keeping in mind its proportion to the flap it resides upon, of course) to shift any number of layers.
The process of enlargement can also be applied to the offset variation of the above category of shifters, if so desired.