In flat-foldable origami, design techniques represented by the circle-river packing approach are effective for complex models but are not suitable for simple models that can be made with a samll number of folds. In this paper, we propose an interactive system for exploring simple origami models by random generation of folded pieces. Our system generates dozens of tiny folded origami pieces and displays them at once. Every time the user requests another set of pieces, different shapes appear, because the generation process includes randomness. By selecting a desired model, the user can obtain the origami instructions to recreate it on real paper.