Tessellation or tiling, uses the same shapes to cover a plane without any overlapping or gaps. It is used in geometry to learn about shapes and areas. Tessellation is also an art form made famous by M.C. Escher, who created various works of art using intricate shapes creating sophisticated patterns. Tessellation can range from elementary shapes, such as triangles and squares, to detailed shapes and figures that fit together like puzzle pieces.
Draw two 2-inch by 2-inch squares on the index card. Cut the squares out.
Cut one of the squares in half to make two rectangles. If cut correctly these rectangles should measure 1 inch by 2 inches.
Cut the other square in half corner to corner to create two identical triangles. If cut correctly, these triangles should have two equal short sides measuring 2 inches.
Trace one of the triangles near the centre of the 8 1/2-by-11 piece of paper. Trace triangles on both sides of the first one working your way outward on the paper until you reach the edges. It should start looking like a mountain range. If a triangle does not fit all the way trace as much of it as possible. Keep in mind that there should not be any gaps or overlaps
Trace triangles on the other sides of the mountain range. Arrange them as puzzle pieces so you end up with two straight edges.
Trace rectangles along the straight edge of the triangles. Match the length to create a crisp pattern. Do this on both sides of the triangles
Repeat the process and continue the pattern of tracing triangles and rectangles until the page is covered in shapes, avoiding gaps or overlaps.
Use a black fine-point permanent marker and a ruler to trace over all the lines on the paper. This will help highlight the shapes after they are coloured in.
Erase any pencil marks before you start colouring to avoid colour bleeds or distortions depending on the medium you are using.
Choose a colour scheme for your tessellation. You can create a colour pattern or colour it randomly.
Always use a finely sharpened pencil. Make your trace marks light. Stick to one medium, such as markers, crayons or coloured pencils. Tape the paper you are tracing on to the table to keep it from shifting and to ensure accuracy. You can create a more intricate design by slightly tilting the paper to one side before you start tracing.
Do not press too hard against the shape when tracing it to avoid warping Do not drag the ruler after you have traced a line because the colour could bleed. Instead lift the ruler up and wipe it with a dry paper towel before you start tracing another line. Make sure marker lines are dry before you start erasing.