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What is a Tessellation?

Karin Jeske Random Tile Patterns Tessellations

Pinnacle Sky Cement Tiles

We often are asked the question, "what does Tesselle mean?" Our company name is derived from the word "tessellation".  A tessellation is the covering of a surface, most often a two dimensional plane, using one or more geometric shapes, with no overlaps and no gaps. Covering a floor or wall surface with tiles is an example of a tessellation.  Common polygons that can easily tessellate are squares, rectangles, triangles and hexagons. The Tessellation above is made from our Pinnacle Hexagonal Cement Tile. Octagons can't tessellate alone, but can when combined with a square.  Within the last century, mathematicians have proven that there are irregular pentagons that can tessellate also. 

As the company founder, I am fascinated with tile patterns that form non-traditional designs. My parents were big fans of M.C. Escher, who created many works of art based on complex tessellations. While working as a consultant and designer in the early 2000s for Interface Flor, I combined my training as a textile designer with the unique ability of a tile to become a module that can create a non-repeating (aperiodic) design when rotated randomly, as opposed to a fabric which requires a repeat to be produced commercially.  I happened upon this when using a then-new software program called Quick Repeat that offered an option to randomly toss a square module.  I quickly learned of others who had made similar discoveries:   Sébastien Truchet, Roger Penrose, and Andreas "Andy" LoewyEdward Borlenghi, a trained architect, and Stu Neyland, a graphic designer, also discovered this method of random tiling through experimentation.  Andy, Edward, Stu and I have shared our experiences of becoming mildly obsessed with this design method. 

Sébastien Truchet (1657 –1729)

Father Sébastian, as he was known, was a French Dominican priest born in Lyon, who lived under the reign of Louis XIV. He was active in areas such as mathematics, hydraulics, graphics, typography, and known for many inventions.  One of his interests was ceramic tile design, and he developed many non-repeating patterns, based on the random rotation of a single module.  His most famous is one that features two quarter circles in a square pattern:

Truchet Tiling

M.C. Escher (1898-1972)

Sometimes referred to as the “father of modern tessellations,” Escher commonly used geometric grids to form intricate interlocking designs. His series Regular Division of the Plane (begun in 1936) is a collection of his tessellated drawings, many of which feature animals. 

Escher Reptiles

Sir Roger Penrose (born in 1931)

The most famous tessellation from this Nobel Prize recipient is the Kite and Dart Tessellation. It provides 2 shapes that can endlessly create random patterns across a surface. This pattern is featured in the form of tile on the floor of The Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University.

Andreas "Andy" Loewy

Andy Loewy, an industrial designer and professor, was awarded a patent  for a method of making a non-repetitive design that did not require symmetry in 1991.  He has since let the patent expire, graciously allowing other designers to use this method.

Andy Loewy Patent

I have posted some of my favorite Tesselle tile designs that can create random patterns in this blog post, but perhaps my all-time favorite random tessellation is the one I created for our 2018 holiday card - click here to see the single module that was rotated across the surface to create this design:

2018 Holiday Card Karin Jeske

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