Project: An Escher-Like Tessellation
The project consists of two parts: a tessellation and a paper.
Create an interesting tessellation.
- The tessellation should be created using the techniques we developed
in class.
- The tessellation should be interesting in the sense that we can analyze
it using the theory of symmetries and isometries.
- The tessellation should be at least 8 X 11 inches (may be larger).
- The tessellation should have some interesting geometry. (A tessellation
with only translational symmetries will not receive an A.)
- The tessellation may be black and white or color, but you should turn
in a finished product. This means no sketches as final product.
- Turn in the finished tessellation, and all preliminary sketches.
Write a paper about tessellations.
- You should think of this paper as a technical paper. Explain everything
you know about the theory of tessellations.
- The paper should be a minimum of 3 pages, typed, double-spaced, 1
inch margins. Figures (and quotes) are excluded from the page count.
- Your paper should cover at a minimum the following topics:
- The theory of tessellations
- The theory of symmetry
- The theory of isometries
- How are Escher-like tessellations created in general?
- How did you create your tessellation?
- What are the symmetry groups for rosettes, borders and tessellations?
- What is the symmetry group for your tessellation?
- Turn in the finished paper, and all preliminary versions.
Grading:
30% Tessellation
You will not be graded on your artistic ability. You should create a nice
finished tessellation that demonstrates that you have put time and effort
into your project. Make sure you use the geometry we discussed in class.
Your tessellation should contain isometries more sophisticated than a translation
to get full credit.
Remember that you can start with a geometric tessellation of any type (including
semi-regular tessellations, or tessellations by tetrominoes or pentominoes).
Feel free to use the computer if you want. This is not a requirement however.
60% Paper
Illustrations can be a good way to help explain the mathematics. Note that
three pages is the minimum. Feel free to write more. Some of the best papers
I have seen have been about 5 pages long. The papers are partially graded
on a curve. This means that you will be compared to fellow students
as well as people who have taken the class before you.
Your paper should of course be grammatically correct and checked for spelling
mistakes.
5% Completeness
Did you turn in preliminary sketches of the tessellation and the drafts
of your paper?
5% In Class Presentation
You will have 5 minutes to show your tessellation. Explain how you created
it (What geometric tessellation did you start with? What isometries did you
use? What does it depict? Why?) Explain what wallpaper group it has. Could
it be adapted to look different? If so discuss that. Did you try other patterns?
What happened if you did?