This simple applet lets you play interactively with the shapes of Penrose tiles that arise using the geometric matching conditions from Section 10.3 of Grünbaum and Shephard. The prototiles are shown on the left, and a sample patch of tiles on the right. You can click on any prototile edge and drag to create a new vertex. Control-click on a vertex to delete it. Drag the sliders below to change the 'tiling vertex parameterization' (details in my dissertation). The two buttons on top reset everything to a new tiling of type P2 (kites and darts) or P3 (rhombs).