How to Do Cool Animal Tessellation Designs

Tiles are often laid in a tessellating pattern.

A tessellation is a pattern that can repeat infinitely along a plane without any gaps or overlaps. While many tessellations are simple geometric shapes, some take the form of fish, frogs, birds or other animals. While these patterns may seem too complex to create on your own, you can use a simple series of steps to transform a self-tessellating shape, such as a triangle, square or hexagon, into an infinitely repeatable design of animal shapes.

Things You'll Need

• Paper
• Red crayon or colored pencil
• Pencil
• Scissors
• Tape

Instructions

1. Cut out a square of paper. Color all four edges of the square to create a red border around its perimeter.

2. Draw a pencil line on the paper. The line can be any shape as long as both ends touch a red edge. For example, you could draw a fish head outline that touches two corners or a bent dog leg that starts and ends on the same edge.

3. 

   Each hole should match a protruding shape in the square's opposite side.

   Cut along the line to divide the square into two shapes. Slide the cut out past the opposite side of the square without flipping or rotating it until the red edges of the cutout and the opposite side of the square meet. Tape the red edge of the cut out to the red edge of the square. For example, if you cut a semicircle out of the left edge of the square, slide it past the right edge to form a bump on the right side that matches the hole in the left side.

4. Continue cutting and taping shapes in the same manner until you are satisfied with the final pattern. Experiment with shapes like legs, fins, heads or wings to see if you can form an animal shape. For example, if your first cut out was a fish head that you cut from the right side and taped to the left, your second and third cut outs could be fin shapes that you cut out of the bottom and tape to the top. You can use the resulting animal shape as a tracing template.

5. Trace the animal template onto a fresh sheet of paper. Slide the template to the right and trace it again, with the edges of the tracings touching. Continue sliding the template up, down, right and left and tracing it to create adjoining tiles of the tessellation. Since each shape taped to one side of the template matches a hole in the opposite side, you should be able to tile the shape indefinitely.

Tips & Warnings

• Remember that every shape you create will form a bump on one side and a gap on the other and try to work it into the animal shape. For example, a fish head protruding on one side could create a gap in the fish's tail on the other side. For more advanced tessellations, you can flip, shift or rotate the shapes before you tape them back on as long as you apply the same rule to every shape you cut out. For rotating tessellations, you can start with a triangle or hexagon instead of a square.

References

• Tessellations.org: Paper Cut Method