Tessellations

People have been fascinated with interlocking designs throughout the ages.  I became interested in this type of design in the 1990’s and diligently studied the work of Dutch artist M.C. Escher to try and figure out how he created his amazing tessellations. One day the light bulb went off and it all fell into place. It is so simple!

 

day lilies closeup (2)

Closeup of Day Lilies

 

Close up of Rhapsody

Close up of Rhapsody

 

The first question is “What is a tessellation?” A tessellation is any shape that can be repeated over and over to fill a surface without gaps or overlaps.

Squares, triangles, hexagons, and diamonds are all tessellations because they can fill a surface without gaps.

 

Shapes

 

Illustration 1 Adjusted

 

 

Those are easy to see, but the more intriguing tessellations contain more complex, interlocking shapes. There are a few rules to follow and these rules must be adhered to or the shape will not “tessellate”.

So the number one rule is that you must begin with a base shape that tessellates. Number two is that you must give it back to the side of the shape that is equal in length. It makes a difference which side you give it back to or whether you flip or rotate the shape. Here are a few designs with this simple square and several of the patterns that can be created by merely putting the cut piece back in different ways.

Lets look at the simplest of the tessellations, the square. It is easy to see how it can repeat over and over to fill a surface without gaps. But what happens if I take a chunk out of that square? It is no longer a tessellation.

 

tessellations illustrations 2

 

tessellations illustrations 3

 

 

So here is the “aha” moment.  The secret to creating tessellations is this: if you take away a piece of a shape, give the piece back to another side of the shape. You will once again have tessellation because the piece you give back will fit into the hole of an adjacent piece where it was taken away.

 

Adjusted illustration

 

illustrations 4b (1)

 

There are a variety of ways to give a shape back and a few rules that must be followed. You can rotate the piece or not depending upon the shape used. I wrote an entire book on this called Designing Tessellations. Unfortunately it is out of print, but it is still available as an “e-book.”

 

Tabs from website

Tessellating Tabbies is available as a kit and pattern on our website.

 

I am currently working on an online class that will be offered through my website sometime in the future. It will cover all the rules, shapes that can be used, how to turn the shape into a usable pattern for quilting and much more!

I’ll keep you posted as to when it will be available but for now, why not come to the Studio and take a class in person. I will be teaching Designing Tessellations August 11 & 12.