Tessellation

M.C. Escher Introduction

We probably would not be studying Tessellations without the works of M.C. Escher. This introductory video will open our class discussion about tessellations. Click the link above to see some of his most popular works on the website that shares his name!

We will begin with direct instruction to make a tessellation pattern that will interlock. The photos below show this instruction step by step.

Step 1 You need a pair of scissors and a note-card.

Step 2 Our first cut will be across the thinnest section. Do not cut extra pieces out of the card, and the cut should go all the way across, see the next photo.

Here is the final cut from step 2, notice if the card was put back together that nothing would be missing. You can cut any shape you want, but you have to be able to put the card back together.

Step 3 Move the card to the other side. I advise you move the card the way I show you in the next series of pictures to avoid any problems. Do not flip either side of the card.

Notice the holes at the top are still at the top. This is so that you can see that I did not flip the card either over or upside down. Tape the card back together. Line up the red line before you tape anything.

Step 4 Now we are going to make a cut long wise.

The same rules apply as before, do not cut excess paper. It must fit back together.

Move carefully as show in this and the next 2 pictures.

You need to line up the cuts so that there is no space, see the next photo

Here you see the cut has no gap and completes a curve, but the cut itself does not stick out.

Tape the pattern, it is now ready to have artwork added. Make sure you put your name on back. These patterns are small and get lost easily.

Make a Design on your pattern

I did not have this design planned when I started. I just made two cuts and started looking at the tessellation pattern like you would a cloud. I typically see a lot of the same things in these patterns, which probably says something about me. I have seen many patterns made over the years and they are all different. Also, note that you can use negative space to fill things that do not quite work with your idea (see the black areas around the feet). This pattern is ready to use to create a Tessellation. For the remainder of this tutorial I will be using a student pattern to show the rest of the steps.

Student Example

Pattern by Diego Sanchez, 2018

This pattern may look nothing like a Pokemon to you, but it worked!

Repeat the pattern on your paper for the entire page, steps shown. There should be no gaps, this is a Daily grade.

Start tracing your pattern in the top left corner of the sheet

The pattern will interlock. Usually it drops a bit each time, see above.

Continue tracing, and be sure to trace the pattern off the page on every side of the paper.

This is what the final page looks like with everything repeated. This will be a daily grade.

At this point, you will be using the light boxes to trace your pattern design onto every pattern on the page. Sometimes the design with only be partly visible. This is normal and should be expected.

Tessellation Project

Here you can see that Diego has finished copying the pattern design on the entire sheet, and they he added color. Diego changed the color for each row, which I think makes this Tessellation easier to look at. I will picture more examples below where that did not occur and I think it is just less interesting overall when the coloring for the design is the same every time you see it repeated.

Artwork by Diego Sanchez, 2018