This is a fairly primitive simulation of Miura-Ori folding made in Processing. A friend made one of these out of an A4 sheet about a year ago and gave it to me. The fact that it survived three or four months in my bag encouraged me to explore its properties further.
This uses Toxiclib’s verletphysics library, as well as Peasycam and ControlP5. It’s a fairly rudimentary simulation, and has problems with self-intersects and spinning off wildly.
The colored lines represent imaginary springs that contract to produce the folds. Minor modification of springs' equilibrium length changes the shape of the overall sheet. Major modification turns the sheet into an origami boulder.
Attempts to put this on OpenProcessing were met with infantile keyboard-smashing and shouting obscene things at a cat.