What is Tessellation?

Tessellation is a pattern of shapes that repeats itself. The shapes are such that they fit perfectly leaving no gaps in between them. Most geometric shapes like triangles, squares, and hexagons tessellate. It can be the same pattern that creates the tessellation or different patterns alternating and repeating itself to create the Tessellations.

M.C. Escher and tessellation

M.C. Escher (born 1898) was a Dutch graphic artist whose art was inspired by mathematics. He created a lot of artwork which involved tessellation. It was the geometric artistry and intricate designs in the Moorish castles of Spain that inspired him to create his artwork. Have a look at some of Escher mathematical art.

How can you make tessellations?

Since tessellation is a form a math art, it is best to draw on a dotted grid paper or graph paper. Using templates created from rectangles or triangles will also help to create tessellations.

Tessellation Art Lesson

1. Geometrical shapes – The best way to start tessellation is creating it with geometrical shapes. Honeycomb is a tessellation that we see in nature. Create tessellations with triangles, polygons, hexagons. Can you create a tessellation with circles? No, since circles next to each other will have gaps.
2. Translation tessellation – Try to slide the pattern to create repetition. This can be best done using a template from a square or a rectangle to interlock patterns. Here is a beautiful video from WhatDoWeDoAllDay where tessellations have been made using the template. Use the same concept to create your own tessellation template.
3. Rotation of the image – Rotational tessellation can also be created using a square or rectangular template. How does the rotational template differ from the translation one? Here when we stick the cut-out pieces from the square, we paste it on adjacent sides of the square instead of the opposite sides as we did during translation tessellation.
4. Try the mirror image or reflection tessellation. Here the images invert either horizontally or vertically. This is best created when using a triangular template.  

After you create the patterns paint them with any medium that you want and add details. Be creative with the shape that you create.

Here are some puzzles and shapes that you can buy from Amazon for tessellations.

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