Just in time for spring.
Click on an image to see what happens.
The idea here is
(1) the opened flower should have much more than twice the surface area of the closed one; it should not just fan out but expand in all directions as it opens.
(2) It must close back reliably the same way.
(3) Should be pretty, and look like a flower.
(4) If possible, it should change dramatically through different stages as it is opened.
(5) The flower must be origami—from a square, no cuts, and glued only to the background card.
The only mechanisms I know of so far (but I’m pretty ignorant) that do any of this reliably are the preliminary fold (opens to 4X; & with a variation, to 9X), the Miura fold (opens to an indefinite multiple of X), and twist folds. All of the flowers shown combine these principles to one degree or another.