2. Create Your Own Tessellation If many copies of a shape can be used to cover a surface, without leaving any gaps between them, then we say that the shape will tessellate. If many copies of a shape can be used to cover a surface, without leaving any gaps between them, then we say that the shape will tessellate. The pattern that is formed is called a tessellation. The pattern that is formed is called a tessellation.

3. Tessellation with Pentominoes

4. Who is famous for tessellations? A man who is famous for his art work with tessellation was Maurits Cornelis Escher, from Leeuwarden, Netherlands. The picture on the right is his self-portrait. A man who is famous for his art work with tessellation was Maurits Cornelis Escher, from Leeuwarden, Netherlands. The picture on the right is his self-portrait. He said, “My work is a game, a very serious game.” He said, “My work is a game, a very serious game.”

5. M. C. Escher Most famous creator of tessellations Most famous creator of tessellations Born in Holland in 1898 (died in 1972) Born in Holland in 1898 (died in 1972) Originally studied architecture before becoming interested in woodcuts and printmaking Originally studied architecture before becoming interested in woodcuts and printmaking Did 137 tessellations in his lifetime Did 137 tessellations in his lifetime

6. Tessellations by M.C. Escher

7. Famous Tessellations This is one of Escher’s most famous tessellations. It is simply called “Reptiles” This is one of Escher’s most famous tessellations. It is simply called “Reptiles”

8. Pegasus (Tessellation 105)

9. *Three Common Transformations *1. Translation, which is a slide of the polygon. * 2. Reflection, which is a flip or mirror image of the polygon. *3. Rotation, which is a turn around one vertex of the polygon. Transformation are an important part of creating tessellations.

10. Transformations Geometric shapes can be translated, reflected, rotated, or glide reflected. Geometric shapes can be translated, reflected, rotated, or glide reflected. These movements of the shapes create a more interesting tessellation design. These movements of the shapes create a more interesting tessellation design. Translation Rotation Reflection Glide Reflection

11. Translations - a slide moves here Get practice template and try creating a translation…. the alteration this side

12. Reflections - mirror images flips here the alteration Get practice template and try creating a reflection….

13. Rotations - turns the alteration rotates around this vertex Get practice template and try creating a rotation... here

14. M. C. Escher, Cycle

15. Bulldog (Tessellation 97)

16. Lizard (Tessellation 104)

17. Make Your Own Escher – like Tessellation Example 1 You need to first create a tessellating template. Step 1: using grid paper cut out a perfect square. Step 1: using grid paper cut out a perfect square. Step 2: with a pencil make a line on two adjacent sides of the square. Be sure not to draw through a corner. Step 2: with a pencil make a line on two adjacent sides of the square. Be sure not to draw through a corner. Step 3: cut out the pieces and attach them with tape to the opposite sides from where they came. Step 3: cut out the pieces and attach them with tape to the opposite sides from where they came.  You have now created your tessellation template.

18. How to make a tessellation template 1234

19. Use your imagination – Can you see the elephant?

20. Seeing a Figure Looking at your tessellation template, study the sides and the shape to decide what sort of figure you might see. Looking at your tessellation template, study the sides and the shape to decide what sort of figure you might see. The person who designed this form saw an elephant and an elf. The person who designed this form saw an elephant and an elf. Are there any other different forms that you might see? Are there any other different forms that you might see? When looking for the shape be sure not to see too much detail as it can make the art work too crowded. When looking for the shape be sure not to see too much detail as it can make the art work too crowded.

21. Putting It All Together Take your tessellation template and trace it on to a piece of paper. Take your tessellation template and trace it on to a piece of paper. When tracing you can use different types of symmetry to change your picture. When tracing you can use different types of symmetry to change your picture. Be sure that your whole page is filled with a repeating pattern. Be sure that your whole page is filled with a repeating pattern. Color in your picture creatively. Color in your picture creatively. Elephants Translation symmetry Elves and Elephants Combinations of symmetry

22. Make Your Own Escher - like Tessellation Example 1 finished

23. Make Your Own Escher – like Tessellation Example 2 Step 1: Start with a simple shape that will tessellate e.g. a rectangle. Step 2: Remove a shape or shapes from one side of the rectangle and fix them to the opposite side.

24. Make Your Own Escher - like Tessellation Example 2 finished

25. Make Your Own Escher – like Tessellation – Example 3 You could start with a hexagon and cut semi-circles from three of the sides and fix them to the opposite sides like this.

26. Make Your Own Escher - like Tessellations – Example 3 Completed

27. Make Your Own Escher – like Tessellations Example 4 Start with a square and cut segments from two sides and fix them to the opposite sides like this.

28. Make Your Own Escher - like Tessellations Example – 4 completed

29. Enjoy making your own tessellations! So, as you can see, tessellations are fun to learn about and easier to make than perhaps, you originally thought. So, as you can see, tessellations are fun to learn about and easier to make than perhaps, you originally thought.