1. “Waterfall,” 1961 by M.C. Escher

2. Tessellations are designs featuring animals, shapes, birds, etc, which can fill the page, without over-lapping, to form a pattern. What are Tessellations The word 'tessera' in latin means a small stone cube. They were used to make up 'tessellata' - the mosaic pictures forming floors and tilings in Roman buildings Here, the term has become more specialized and is used to refer to pictures or tiles, mostly in the form of animals and other life forms, which cover the surface of a plane in a symmetrical way without overlapping or leaving gaps. The tilings in the Alhambra in Spain were laid out by the Moors in the 14th century. They are made of colored tiles forming patterns, many truly symmetrical. By our definition, they are not tessellations but they did inspire the young M.C Escher, who copied them into his notebooks and later converted some into true tessellations. A Roman bull mosaic Escher's drawing of Alhambra tiling.

3. Maurits Cornelis Escher can be regarded as the 'Father' of modern tessellations. He is famous for his impossible depictions like the one on the right, but he was a master of lino and wood cuts and produced many superbly crafted landscapes as well.

4. If you look at a completed tessellation, you will see the original motif repeats in a pattern. Two possibilities shown here are in a line facing one way, and then in a line facing the other, or, it may be in a whorl of rotated instances. This is symmetry. There are 17 possible ways that a pattern can be used to tile a flat surface or 'wallpaper'

5. There are 4 ways of moving a motif to another position in the pattern.

6. Which of the four ways did Escher use to get the image to move into the next position? What is Escher trying to say in this piece called, “Encounter” ?

7. Your tessellation must be based on a shape that will tessellate. Look at the foxes. Can you see the geometric shape they are based on?

8. So what shapes will tessellate? There are only 3 regular geometric shapes that will. 'Regular', means that all sides and internal angles are equal. These are the equilateral triangle, square and hexagon. The 'F's show that the shapes can be flipped and rotated without affecting the ability to tessellate. This can make whole pictures more varied and interesting. Not all the possibilities are shown here.

9. Other well known geometric shapes that will tessellate are the rectangle, parallelogram, and diamond (or rhomboid). Note that the parallelogram and diamond can be squashed or thick, it makes no difference to their ability to tessellate. The parallelogram could have alternate rows tipped the other way.

11. If we overlay a grid, you can see how each individual picture is based on an equilateral triangle. You can start off making your own personalized Tessellation by taking one of the regular Geometric shapes like an Equilateral triangle, square or hexagon and cutting away sections in order to make another shape. Such as taking a Equilateral triangle that turned Into a Calf’s head.