Creating Tessellations

Creating Tessellations

The Magic of M.C. EscherThe Magic of M.C. Escher

A Biography of M.C. Escher

A Biography of M.C. Escher

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A master at creating tessellations

What is a tessellation?What is a tessellation?

Defenition:a shape being repeated over and over again covering a plane, or area leaving no gaps or overlapping…..like the squares below.

Defenition:a shape being repeated over and over again covering a plane, or area leaving no gaps or overlapping…..like the squares below.

There are four types of tessellating patterns

There are four types of tessellating patterns

rotation translation reflectionand glide reflection

rotation translation reflectionand glide reflection

Tessellations help us to relate to the mathematical

world

Tessellations help us to relate to the mathematical

world

Through symmetry

Today we will start by creating our own

tessellating pattern

Today we will start by creating our own

tessellating pattern

Step 1: Start by opening a photoshop document

Step 1: Start by opening a photoshop document

File>New>

Preset>Letterclick OK

(make sure to add a title to your work)

Step 2Step 2 Go to View>click on Rulers

Make a new layer: click on layer> new> layer Click on the Rectangular Marquee tool Create a box that is 2” inches square, hold shift

while using the mouse..this will ensure that he box stays equal on all sides

Choose the paint bucket> choose a color and fill the box

Choose select> deselectYou now have your first square

Go to View>click on Rulers

Make a new layer: click on layer> new> layer Click on the Rectangular Marquee tool Create a box that is 2” inches square, hold shift

while using the mouse..this will ensure that he box stays equal on all sides

Choose the paint bucket> choose a color and fill the box

Choose select> deselectYou now have your first square

Step 3Step 3 Use your move tool, shaped like an arrow at the top of

the tools palette and move your box to the center of your page

Choose the eraser tool> select a #5 with a solid hardness

Now erase a curvy, jagged, individual line…don’t get to crazy right now…keep it simple….On the left side of the box

Now use your selection tool(the magic wand) and select the left most shape of the box(it should have a moving dotted line around it)

Choose Edit> Cut> Paste….your shape should be on a new layer……

Now use your move tool and place this shape on the exact opposite side of the “old” square from where you cut it out

Use your move tool, shaped like an arrow at the top of the tools palette and move your box to the center of your page

Choose the eraser tool> select a #5 with a solid hardness

Now erase a curvy, jagged, individual line…don’t get to crazy right now…keep it simple….On the left side of the box

Now use your selection tool(the magic wand) and select the left most shape of the box(it should have a moving dotted line around it)

Choose Edit> Cut> Paste….your shape should be on a new layer……

Now use your move tool and place this shape on the exact opposite side of the “old” square from where you cut it out

Step 4Step 4 Now it is time to repeat the process from step

three but this time cut a shape from the top and move it to the bottom side of the “old” square

Now, you should have 4 layers…… a background, layer 1, 2, and 3

We want to merge the three layers so we will have only two…….

Make sur e your top layer is selected or highlighted blue, Press and hold command/apple key and then push the letter “E” twice.

You should now have two layers… a background and layer 1

Now it is time to repeat the process from step three but this time cut a shape from the top and move it to the bottom side of the “old” square

Now, you should have 4 layers…… a background, layer 1, 2, and 3

We want to merge the three layers so we will have only two…….

Make sur e your top layer is selected or highlighted blue, Press and hold command/apple key and then push the letter “E” twice.

You should now have two layers… a background and layer 1

Step 5Step 5

Now comes the creative part………look at your “organic shape” and try to imagine that shape becoming something unique, interesting, crazy, cool

Add lines with your eraser tool or choose the pain brush and add what ever comes to your mind

Try to think back to the video of M.C. Escher….. Look around the room for ideas Use your imagination

Now comes the creative part………look at your “organic shape” and try to imagine that shape becoming something unique, interesting, crazy, cool

Add lines with your eraser tool or choose the pain brush and add what ever comes to your mind

Try to think back to the video of M.C. Escher….. Look around the room for ideas Use your imagination

Step 6Step 6

Once you have your creation we need to make a selection of it….

Hold the apple key and hover your mouse over the thumbnail of layer 1

Click the mouse and your image should have a dotted line around it…?

Once you have your creation we need to make a selection of it….

Hold the apple key and hover your mouse over the thumbnail of layer 1

Click the mouse and your image should have a dotted line around it…?

Step 7Step 7 Making copies and arranging your subject Once you have your selection you can copy and paste or hold

the apple key and press “C” to copy and then keep holding the apple key and press “V” to paste. Do this multiple times and you will have multiple copies on multiple layers

With Photoshop…layers are a good thing

Making copies and arranging your subject Once you have your selection you can copy and paste or hold

the apple key and press “C” to copy and then keep holding the apple key and press “V” to paste. Do this multiple times and you will have multiple copies on multiple layers

With Photoshop…layers are a good thing

Step 8Step 8 Arrange your shapes to create you tessellation Arrange your shapes to create you tessellation

Step 9Step 9 Saving your work Depending on what you plan on doing with this

work…you should save accordingly. First File> Save as> Jpeg (full size, high resolution

for large prints) save to a folder on desktop We will then go to image> image size> pixel

dimensions…..change the largest dimension to 900 pixels. You should see the Megabytes (MB) change from 24.1mb to 1.79mb. This is a good size for us as we are posting our work on the MOODLE website.

Click ok File> save as> format=jpeg> save

Saving your work Depending on what you plan on doing with this

work…you should save accordingly. First File> Save as> Jpeg (full size, high resolution

for large prints) save to a folder on desktop We will then go to image> image size> pixel

dimensions…..change the largest dimension to 900 pixels. You should see the Megabytes (MB) change from 24.1mb to 1.79mb. This is a good size for us as we are posting our work on the MOODLE website.

Click ok File> save as> format=jpeg> save

Step 10Step 10

Make sure to save a high resolution image and the smaller image for posting on the internet

Post your smaller image under 2mb on moodle

Make sure to save a high resolution image and the smaller image for posting on the internet

Post your smaller image under 2mb on moodle

You should have a complete Tessellation that looks interesting to say the least…the options are endless!

Maybe you can become the next master like Escher!

Special thanks for inspiration and

information:

Special thanks for inspiration and

information:

http://www.mcescher.com/ http://mathforum.org/sum95/suzanne/whattess.ht

ml http://www.ims.k12.nj.us/Webquests/tesselation/te

sselation.htm http://mathforum.org/~sanders/geometry/GP08Cre

atingTessellations.html

http://www.mcescher.com/ http://mathforum.org/sum95/suzanne/whattess.ht

ml http://www.ims.k12.nj.us/Webquests/tesselation/te

sselation.htm http://mathforum.org/~sanders/geometry/GP08Cre

atingTessellations.html