The Creation of a tessellation

I love tessellations and am intrigued by the intersection of math and art. For those of you who are wondering what a tessellation is, the easiest way I can explain it is, M.C. Escher. A great deal of Escher's art included tessellations. Tessellations are geometric shapes that connect together to tile a plane without any gaps in between them. A square is a great example. You can place squares next to each other and tile a plane with squares and there would not be any gaps in between the squares when they are stacked up. Not all geometric shapes will tessellate. Circles, as an example, will not tessellate because when you stack them up next to each other, there will be gaps around the shapes.

I often talk about my love of tessellations when teaching rug hooking. At the Rock River Rug Retreat in 2017, we had a discussion about tessellations which intrigued many of my students. When I went back to teach at the same camp in 2018, I had several students ask if I would talk again about tessellations and several asked if I could design a small tessellation for them. Let the fun begin!

For the requested design, I came up with School of Fish which was tessellated from a square using the rules of taking away from the square and re-gifting the take-away to another area on the square. I was pleased with the results and I love my new pattern, "School of Fish". While playing around to develop School of Fish, I did some cutting and re-gifting just for fun which is where I came up with the shape that evolved into Rock River Tessellation. I put the pattern onto backing and took it to the 2018 Rock River Rug Camp to include in part of my discussion. At camp, my students asked for me to blog about the process of creating and developing this pattern and so here we are!

I developed Rock River Tessellation by first starting with a square.

1. Start with a square cut from a piece of card stock

1.

2. Draw a line running from side to side and another line running from top to bottom

3. Cut on the lines to create four separate pieces.

4. Rearrange the four cut pieces so that the corner edges meet in the middle. Tape.

5. This is your tessellated shape. If you repeat this pattern to the left, right, top or bottom, the pieces will now interconnect.

6. I now transfer the shape onto a piece of quilters

template to create a more durable pattern for my

tessellation.

7. Create your rug pattern on your backing by using

the piece of quilters template, start in the middle of

the pattern and trace around the template. Continue

by moving the template to the sides, top and bottom

by lining up the already drawn line from the first drawn

shape and then continue to trace the other edges.

When transferring your pattern onto your backing

be very careful to ensure that the pattern is drawn

straight.