Tessellations

Surrounding myself with a group of dutch people, drinking dutch water, and breathing dutch air for a long weekend, my brain must have switched to dutch thinking. Read more about this incredible weekend at the end of this blog post.

Dutch graphic artist M. C. Escher (also known for his tessellated lizards) inspired me to do a write-up on tessellations. The first tessellations, however, can be dated back to 4000BC.

There are various types of tessellations:

    • Regular
    • Semi-Regular
    • Demi-Regular Tessellations
    • Non-Regular or Irregular Tessellations

There are only three Regular Tessellations. The first one being the square grid, second the grid created with equilateral triangles, and the Hexagonal grid.

This week we will focus on Semi-Regular Tessellations.

There is a lot of information readily available on the internet. For very in-depth information, I recommend reading through “The Hardness of Finding Hamiltonian Cycle in Grids Graphs of Semiregular Tessellations” by Kaiying Hou, published December 2017.

Semi-Regular Tessellations can be the base for many new patterns. There are 8 different semi-regular tessellations. This week I will introduce 2 of them that are very well suited for tangling:

Tessellation 3636 CPT Base Pattern

As I am not a fan of making up names, I tried to find a common reference for these Tessellation patterns. Mathematicians differentiate by counting the sides of the shapes meeting at the intersection (vertex). So the 3.6 means a Triangle is sharing a connecting point with a polygon. A shape with 3 sides meets a shape with 6 sides. This particular grid is also known as the Isometric Grid.

As with all grid-based patterns, Tessellation 3.6.3.6 can also be used as a ribbon-style pattern.

Tessellation 3.6.3.6 as a ribbon

The shapes can be filled in so many different ways. And depending on what CPT Technique you apply, the base pattern will change completely.

Tessellation 3.6.3.6 fill options

Tessellation 4.8.8 shows that the vertex connects a 4 sided shape with 8 sided shapes.

Tessellation 4.8.8 CPT Base Pattern

Again, there are so many possibilities to play with the pattern. I included a few examples on the step-out. Of course, there are many more possibilities!

Ellen Wolters created a video, demonstrating a lot of additional options. If you have been wondering how to apply the different CPT Techniques to a base pattern, don’t miss the video!

Tessellation CPT Session by Ellen Wolters Tessellation CPT Session by Ellen Wolters

A variation of Tessellation 4.8.8 can also be found in Octagon Tessellation:

Octagon Tessellation by Ina Sonnenmoser


Our tangle weekend in the Netherlands was AMAZING! Instead of spreading virtual hugs, we were able to give each other REAL hugs!

Due to privacy issues, I won’t post any photos of the tanglers, but have a look at the incredible artwork we created together! Each piece looks completely different. One would never guess that all these Mandalas were created in the same class. Creativity at it’s best!

Travelling Mandala

Watching how tanglers grow and face up to challenges made me decide to hold more classes in person. Right now I am planning a CPT seminar during the weekend November, 9 and 10 in Los Angeles. Mark the date in your calendar if you want to attend!

More details to follow soon!

Hugs,
Ina

One thought on “Tessellations

  • August 31, 2019 at 8:06 am
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    AWE inspiring, just beautiful and so creative, thank you for sharing!

    Reply

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