Using the applet below, you may place Penrose rhombs adjacent to one another following Penrose's matching rules. Simply select whether you wish to lay down a thick or thin rhomb using the menu at the bottom. Then click on the edge of an existing rhomb to which you would like to join the next rhomb. Existing rhombs may be removed by selecting the red X from the menu and clicking in the center of the rhomb you wish to remove.
The applet below can help you to construct a Penrose tiling. Rhombs may be added as in the applet above. However, a check is performed to determine if the resulting configuration may be extended to create a Penrose tiling, and, if not, the rhomb is not added. Furthermore, tiles that must be added are shown in gray as are the outlines of tiles from the inflation hierarchy.