Tessellations are identical figures that can fill a flat plane without leaving gaps. Essentially, they are like puzzle pieces, except each piece is identical to every other. They are popular for use in tiling and in the works of famous artists, particularly M.C. Escher. Creating your own tessellations can be a rewarding experience by producing new forms and finding new uses for space.
Instructions
1. Measure and mark out a perfect square from your card stock. Using your pen and ruler, make sure that the square's height and width are the same. Cut out the square.
2. Select one horizontal and one vertical edge. These will be your design edges. The opposite sides will be your application edges.
3. Draw a design on your two design edges with the pen. The goal is to have a shape that can be cut out of the design edge. This design will be your negative space, which is removed but accepting of an identical positive space from another tile. For example, if you cut a triangle from an edge you would have negative space in the shape of a triangle. In later steps, you will be filling this negative space with an identical positive space from the opposite design edge. Therefore, the shape must be continuous, with its beginning and end points both on the design edge. Make sure that your two designs, one on the horizontal and one on the vertical, do not interfere with each other.
4. Cut your design out of the design edge using your utility knife. It is very important that there are no tears, otherwise your tessellations will not fit together properly. Save the cut-out portion in one unblemished piece.
5. Tape the cut out design from each design edge on to the application edge directly across from it. Tape the design flush with the edge. Your application edges should now look like positive images of your design edge's negative space. Your basic tessellation template is complete.
6. Use your tessellation as a template for cutting out additional tessellations. Trace around your template onto card stock, then carefully cut out with the utility knife. The more precise your reproductions, the more effectively your tessellations will fit together.
