Sunday, May 18, 2014

Doing Math: Geometric Tessellation

For this week's post I decided to create a geometric tessellation. You might think drawing repeating patterns would be pretty easy, but as each pattern is added the lines start to cause confusion and mistakes are most likely to be made. My eraser was a much needed tool in completing this tessellation. The one shown below took me about and hour and 45 minutes to make and with the help of just a solo cup and a ruler I must say I am proud of it, though it is not very precise.
Step 1:
With not having a protractor or compass I had to use a cup as a starting point. I traced a circle around the base of the cup and then inscribed a hexagon in to that circle using a ruler to try to make the sides as equal in length as possible. I went off of this hexagon for the rest of them and just a ruler to align the overlapping hexagons. I chose to start with a hexagon of this size as it leaves a fair amount of open space to add more details without loosing the contour of each shape added.

Step 2:
Next I added a smaller hexagon at 3 vertices of the each of the larger hexagons. Then I added irregular hexagons inside some of the larger hexagons as shown above, making sure to repeat this pattern. I knew I wanted to center some polygon around some of the vertices of the large hexagons and adding the smaller hexagons was just the thing to do. Once I did this I thought I would continue with the hexagon theme and fill in the space of the larger hexagons. I held back a little bit to get the "every other" pattern going.

Step 3:

For the finishing touch I outlined every line in sharpie for a more pronounced look and to clearly see the repeating pattern.

Tessellations can be just beautiful pieces of art but they also appear in nature and other everyday items. For instance, honeycombs, floor tilings, glass ceiling framework, and brickwork all incorporate patterns that define a tessellation. Since these are such intriguing designs it is not surprising that marketing and advertising companies use them on packaging and products to grab a consumer's attention. It might be a small pattern but I believe that you will always be able find a tessellation in your everyday life.


  1. Cool pattern. I like the primitive tools aspect.
    clear, coherent:+
    complete, content: it would be good to hear your design thinking - some of the whys behind your choices. That would probably relate to the mathematical characteristics of the pattern you made.
    consolidated: Think about how to summarize. One framework to use to summarize is answer one or more of: what? (important bits) so what? (why important) or now what? (what's next).

  2. I really like how you started with rhombi and went from there. This is amazing for it being freehand! I really like how you use two pictures to really show the detail involved in the tessellation.

  3. Hi Morgan, I am doing a website for a new Structural Engineering firm, and have spent about an hour and a half today looking at repeating patterns trying to find something that has the right structural feel but still also has enough interest. I think your Geometric Tessellation is just what I've been looking for! Of course first I need your permission and then my clients' approval. We would of course put a credit in one of the corners of the screen. Let me know what you think.