Tessellations
SOI: Social constructions of reality change patterns we perceive as beautiful.
Factual: What is a tessellation? What three regular polygons tessellate? What three transformations can be applied to create tessellations?
Conceptual: How does society determine what is beautiful? In what ways can math inspire art?
Debatable: Is math beautiful?
Factual: What is a tessellation? What three regular polygons tessellate? What three transformations can be applied to create tessellations?
Conceptual: How does society determine what is beautiful? In what ways can math inspire art?
Debatable: Is math beautiful?
What is a tessellation?
Tessellations are created when a shape repeats over a plane without gaps or overlaps. Complex tessellations are common in Islamic art, exemplified by the Alhambra Palace in Andalusia, Spain. M.C. Escher became famous for his artwork exploring tessellating shapes, finding inspiration from the complex tile work and carved tessellation relief sculptures he encountered on a trip to the palace.
We will be using Illustrator to create a series of irregular tessellations, exploring a variety of methods to approach this task.
For your second demonstration grade, you will choose one of the methods covered in class, and create a full color, detailed tessellation using Adobe Illustrator.
Here is a link to the presentation we viewed in class to introduce the unit.
We will be using Illustrator to create a series of irregular tessellations, exploring a variety of methods to approach this task.
For your second demonstration grade, you will choose one of the methods covered in class, and create a full color, detailed tessellation using Adobe Illustrator.
Here is a link to the presentation we viewed in class to introduce the unit.
Creating an Irregular Tessellation with a Square
We used a square as a template to create an irregular tessellation, following the steps below.
Step 1: Open a new Letter size document, landscape orientation. Draw a 200pt by 200pt square.
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Step 2:Lock the square layer, make a new layer. Use the pen tool to draw a line across the top of the square, from corner to corner. Click on the black arrow tool.
Hold the OPTION key, click on the line, drag to the bottom of the square. |
Step 3: Lock the second layer, make a new one. Use the pen tool to draw a line on the left edge of the square, from corner to corner. Click on the black arrow tool. Hold the OPTION key, click on the line, drag to the right edge of the square.
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Step 4: Turn off the square layer (click on the "eye"). Unlock the second layer.
Select all of the lines and go to Object > Path > Join |
Step 5: Use the pencil tool to add details, drawing what you "see." It will be weird. That is okay!
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Step 6:
Select all. Go to Object > Live Paint > Make. Choose ONE COLOR to paint in the drawing. You can change the saturation and value (the S and the B). |
Step 7: Hold the option key, and drag the drawing to the left (use the black arrow tool).
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Step 8: Use the eyedropper tool to select a color in your drawing. In the color menu, select "Compliment." Fill in the drawing on the left with that color. You can change the S and the B, but NOT the H.
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Step 9: Hold the option key and click and drag to repeat the drawing so that it fills the document. Alternate the colors.
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Other Types of Tessellations
The class will divide itself into groups of four. Within each group, one person will research one type of tessellation from the list below, and then attempt to create that type of tessellation using Illustrator. You will have two days to work on your assigned problem before you have to teach your group how to complete the tessellation. In the end, everyone will be responsible for creating one of each of the tessellations listed below.
Irregular Tessellations from a Triangle (Persons 1 and 2)- Create a tessellation using an equilateral triangle as the base. You must alter all three sides.
Hints: You will need to discover how to make an equilateral triangle in Illustrator (Google it)! You will also need to rotate lines with precision. Go to Object->Transform ->Rotate and choose the appropriate angle (you might need to use a little math, or just "undo" until you get it right). Last, you will have to precisely determine an exact midpoint for one of the sides of the triangle. Tessellations from Pentominoes and 7-Pin Polygons (Person 3)- While this seems like more work because you are researching two different types of tessellations, both of these are fairly easy to understand and create tessellations with. (You do not need to create any "squiggly" lines, but you do need to know how to create two different tessellations- one pentomino tessellation, and one 7-pin polygon tessellation). You should also be able to answer these questions: Do all pentominoes tessellate? Do all 7-pin polygons tessellate? Are there pentominoes or 7-pin polygons that require transformations other than translation in order to tessellate? Irregular Tessellations from a Square, using Rotation or Glide Reflection (Person 4)- You will create an irregular tessellation starting with a square. Instead of translating the "squiggly" lines, you will try rotation or glide reflection transformations. You do not have to know how to do both. Also, you do not need to add details- just concentrate on the overall shape of the tile. Hint: As with Persons 1 and 2, you will also need to rotate lines and shapes with precision. Go to Object-> Transform -> ("Rotate" or "Reflect"). |
Every student must create her own triangle, pentomino, 7 pin polygon, and rotation or glide reflection square tessellation. None of the tessellations need "details," but you should alternate between two colors, so the tile is easily discerned. You will post these four tessellations in a gallery element, with the name of the tessellation labeled in the "caption," like this:
Final Tessellation-10pts
You will be choosing one of the types of tessellations you studied to make a final, refined version of... think details, complex patterns, something that takes more than 10 minutes to make. This final tessellation will be due Tuesday, 3/22.
Benchmarks:
Benchmarks:
- No gaps or overlaps- it's a true tessellation
- Turned in on time (Tuesday, 3/22)
- Used classtime wisely (Finished "early?" How can you improve your tessellation?)
- Uses 3 or more colors.
- Fills the page.
- It is original.
- It is creative. (if you chose a pentomino or 7 pin polygon, how can you make it more than just a simple shape? Coloring is not enough.)
- It has details or it is intricate in its design.
- You used something you previously learned in class- and labeled the image with what type of tessellation used.
- You used the "artboards" option when you saved it as a jpg, and posted it on weebly with "enable lightbox" checked. It is titled "Final Tessellation."