CONGRUENT SHAPES (Tessellations)


Spring, 2010
Fall, 2009


To develop a repeating pattern of congruent shapes where the positive shape creates the negative shape and the negative shape creates the positive shape. This project will encompasses design principles such as shape manipulation, symmetry / asymmetry, positive / negative shape, and figure / ground relationships. We will define and discuss these principles in class.

"A tessellation is a collection of shapes called tiles that fit together without gaps or overlaps to cover the mathematical plane. The Dutch graphic artist M.C. Escher became famous for his tessellations in which the individual tiles are recognizable motif such as birds and fish". Robert Fathauer

Shape - to embody in definite form. An enclosed space.
Symmetry - the property of being symmetrical; especially : correspondence in size, shape, and relative position of parts on opposite sides of a dividing line or median plane or about a center or axis — compare bilateral symmetry, radial symmetry
Asymmetry - not symmetrical, but still may present a sense of balance
Positive shape - we call the figure or foreground shape positive and the focus of the picture, it is often called the subject matter (usually)

Negative shape - this is usually an empty shape or space and is the background or surround of the subject matter
- the part of a composition that we pay attention to is called figure. The figure is also called a positive shape.
Ground - everything that is not figure is ground.


Graph paper
Sketch Pad
Illustration Board (hot or cold pressed) (20 x 15 inches)
Micron Pens
India Ink
Brushes (must bring with you next class)
Measuring tools
Exacto Knife


Start with a simple tessellation shape like a grid. Within the grid you could have a square, rectangle, parallelogram, octagon, etc. The idea is to use a shape that will not leave a space between the shapes when aligned together. To understand the idea, start using graph paper. This allows you to explore several ideas while using precise measurements. The idea is to divide your shape diagonally, vertically, or horizontally. What you do to one side of the separation, you repeat on the other side. What you subtract from the shape, you add to the shape in a symmetrical fashion. Similar to your prior project, you will deconstruct and reconstruct your shape with intent to create repeating congruent positive and negative shape. Your final goal is to make an unusual design where the positive creates the negative and the negative creates the positive.

-Use cut paper to freely move your shapes around. This will initiate ideas / evolution, and allow you to work in a mechanical approach (this may activate another part of your thinking process).


Canvas size: 20 x 15 inches
Image size: 16 x 12 inches
On the back of your work / illustration board show the initial shape used, and the reconstructed shape (two shapes).
If you use squares, parallelograms, rectangles, etc., do not make your shapes any larger than 2 inches (2 inches is a good size to work with).
No dogs or cats or any recognizable objects (Escher's work is visually stimulating, but I am not looking for Escher-esque work). Focus on design (non-objective).
The positive and negative shape must be congruent shapes.
Draw out your plan using an H4 pencil, and full in the shapes using your micron pens. Micron pens are for the borders of shapes and the India ink is for the interior of larger shapes. Your goal is to end up with an even, rich black (CRAFTSMANSHIP, practice first!!).


-Are you following the concept of project?
- Does your work conceptually stimulate the viewer?
- Neatness, precision, Intelligent and crafty use of the medium.
-Originality, problem solving, developed idea
Composition (overall design)
Does your work visually stimulate the viewer?
-Does the project seem complete, developed/evolved, and well executed?


Below is an example of the finished project slightly altered to how you are to submit your final version (the shape source will be placed on the back of your work).




Below is a simple example of how to create a congruent shape that creates itself in the negative(aka-ground).