Create Your Own TessellationCreate Your Own Tessellation

• If many copies of a shape can If many copies of a shape can be used to cover a surface, be used to cover a surface, without leaving any gaps without leaving any gaps between them, then we say between them, then we say that the shape will that the shape will tessellatetessellate..

• The pattern that is formed is The pattern that is formed is called a called a tessellation.tessellation.

Tessellation with PentominoesTessellation with Pentominoes

Who is famous for Who is famous for tessellations?tessellations?

• A man who is famous A man who is famous for his art work with for his art work with tessellation was Maurits tessellation was Maurits Cornelis Escher, from Cornelis Escher, from Leeuwarden, Leeuwarden, Netherlands. The Netherlands. The picture on the right is picture on the right is his self-portrait.his self-portrait.

• He said, “My work is a He said, “My work is a game, a very serious game, a very serious game.”game.”

M. C. EscherM. C. Escher

• Most famous creator of Most famous creator of tessellationstessellations

• Born in Holland in 1898 Born in Holland in 1898 (died in 1972)(died in 1972)

• Originally studied Originally studied architecture before architecture before becoming interested in becoming interested in woodcuts and woodcuts and printmakingprintmaking

• Did 137 tessellations in Did 137 tessellations in his lifetimehis lifetime

Tessellations by M.C. EscherTessellations by M.C. Escher

Famous TessellationsFamous Tessellations

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

PegasusPegasus

(Tessellation 105)(Tessellation 105)

*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.

TransformationsTransformations

• Geometric shapes Geometric shapes can be translated, can be translated, reflected, rotated, reflected, rotated, or glide reflected.or glide reflected.

• These These movements of the movements of the shapes create a shapes create a more interesting more interesting tessellation tessellation design.design.

Translation

Rotation

Reflection

Glide Reflection

Translations - a slide

moves here

Get practice template and try creating a translation….

the alteration

this side

Reflections - mirror images

flipshere

the alteration

Get practice template and try creating a reflection….

Rotations - turns

the alteration

rotates aroundthis vertex

Get practice template and try creating a rotation...

here

M. C. Escher, M. C. Escher, CycleCycle

BulldogBulldog

(Tessellation 97)(Tessellation 97)

LizardLizard

(Tessellation 104)(Tessellation 104)

Make Your Own Escher – like Make Your Own Escher – like Tessellation Example 1Tessellation Example 1

You need to first create a tessellating template.You need to first create a tessellating template.

• Step 1Step 1: using grid paper cut out a perfect square. : using grid paper cut out a perfect square.

• Step 2:Step 2: with a pencil make a line on two adjacent with a pencil make a line on two adjacent sides of the square. Be sure not to draw through a sides of the square. Be sure not to draw through a corner.corner.

• Step 3:Step 3: cut out the pieces and attach them with cut out the pieces and attach them with tape to the opposite sides from where they came.tape to the opposite sides from where they came.

You have now created your tessellation template.You have now created your tessellation template.

How to make a tessellation How to make a tessellation templatetemplate

11 22 33 44

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

Seeing a FigureSeeing a Figure• Looking at your tessellation template, study Looking at your tessellation template, study

the sides and the shape to decide what sort of the sides and the shape to decide what sort of figure you might see.figure you might see.

• The person who designed this form saw an The person who designed this form saw an elephant and an elf.elephant and an elf.

• Are there any other different forms that you Are there any other different forms that you might see?might see?

• When looking for the shape be sure not to see When looking for the shape be sure not to see too much detail as it can make the art work too much detail as it can make the art work too crowded.too crowded.

Putting It All TogetherPutting It All Together• Take your Take your

tessellation template tessellation template and trace it on to a and trace it on to a piece of paper.piece of paper.

• When tracing you can When tracing you can use different types of use different types of symmetry to change symmetry to change your picture.your picture.

• Be sure that your Be sure that your whole page is filled whole page is filled with a repeating with a repeating pattern.pattern.

• Color in your picture Color in your picture creatively.creatively.

Elephants

Translation symmetry

Elves and Elephants

Combinations of symmetry

Make Your Own Escher - like Tessellation Make Your Own Escher - like Tessellation Example 1 finishedExample 1 finished

Make Your Own Escher – like Make Your Own Escher – like Tessellation Example 2Tessellation 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.

Make Your Own Escher - like Make Your Own Escher - like Tessellation Tessellation

Example 2 finished Example 2 finished

Make Your Own Escher – like Make Your Own Escher – like Tessellation – Example 3Tessellation – 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.

Make Your Own Escher - like Make Your Own Escher - like Tessellations – Example 3 Tessellations – Example 3

CompletedCompleted

Make Your Own Escher – like Make Your Own Escher – like Tessellations Example 4Tessellations Example 4

Start with a square and cut segments from two sides and fix them to the opposite sides like this.

Make Your Own Escher - like Make Your Own Escher - like Tessellations Tessellations

Example – 4 completedExample – 4 completed

Enjoy making Enjoy making your own your own

tessellations!tessellations!

So, as you can see, tessellations So, as you can see, tessellations are fun to learn about and easier are fun to learn about and easier

to make than perhaps, you to make than perhaps, you

originally thought. originally thought.