Abstract In this expository paper, we present some fundamental connections between iterated function systems, in particular those whose attractors are the graphs of multivariate real-valued fractal functions, and foldable figures, affine Weyl groups, wavelet sets.

Abstract Origami, the ancient art of paper folding, embodies techniques for transforming a flat sheet into shapes arbitrary complexity. Although this makes origami conceptually attractive source inspiration when designing foldable structures and reconfigurable metamaterials multiple functionalities, their designs are still based on set well-studied patterns leaving full potential inaccessible d...

A simple model of deploying tree leaves is assembled in different arrangements to produce polygonal foldable membranes for use as deployable structures. One family of folding patterns exhibits a small strain mechanism, which is investigated. Variations on the basic arrangements can be used to fold membranes with a discretized curvature.

We show a novel design method of one-DOF deployable mechanism based on a space curve, through creating a curved folding and discretizing the folding into rigid origami. By interpreting constant angle curved folding as a flat-foldable quadrilateral mesh origami, we design novel irregular tessellated, cylindrical, and cellular flatly collapsible structures, whose behavior is easily controlled by ...

A variable stiffness fiber made of silicone and low melting point alloys quickly becomes >700 times softer and >400 times more deformable when heated above 62 °C. It shows remarkable self-healing properties and can be clamped, knitted, and bonded, as shown in a foldable multi-purpose drone, a wearable cast for bone injuries, and a soft multi-directional actuator.

We establish a correspondence between the invariant subsets of a non-degenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside structure. Moreover, we introduce the notion of a foldable solution, which extends the one of a decomposable solution. AMS Subject Classification: 16T25, 20F36.

The capsule of the crystalline lens, if sufficiently present, is used as a support tissue for intraocular lens (IOL) implantation surgery performed on vitrectomized eyes. Eye trauma or iatrogenic damage during complicated cataract surgery, loss of position and zonule connections of the crystalline lens, and IOL via dislocation may cause loss of support tissue for lens capsule implantation prior...