Lesson 3:
Block printing in class

Lesson 1
Ritual Geometry


Lesson 2
Group Elements

Color Theory

Lesson 3
Groups and Groups Acting on Sets

Block printing

Lesson 4
Klimt and the Computer

Color and symmetry in modern art I

Lesson 5

Islamic art

Lesson 6
Penrose and Rice

Color and symmetry in modern art II

Lesson 7
Escher 1

Escher 2

Lesson 8
Hundertwasser & Griffeath

Pattern and Modern Painting

Brian P. Hoke: Cellular Automata and Art

Student's Work



A 2-dimensional motif can repeat in only four different ways. These four types of repetition or symmetry operations are:

1) Translation - one motif moves up or down, left or right or diagonally while keeping the same orientation.

2) Rotation - the motif turns

3) Reflection - the motif reflects, as in a mirror

4) Glide reflection - the motif translates and reflects.


If you rotate one fundamental region around a point you can superimpose it exactly on another fundamental region. The center of rotation is called a roto-center. Distant centers of rotation produce apparent translations. Roto-centers can be in the center of a unit cell line.


The image reverses as in a mirror. Mirror lines divide areas of reflection. With translation or rotation, the image at the start can be directiy superimposed on the image at the finish, or anywhere along the way. Reflection lacks this continuity. The motif does not stay on the surface of the plane, it flips over. Because it flips rather than glides, it is called an indirect or improper operation. Rotation and translation which involve displacement are called direct or proper operations.


Glide reflection is an indirect operation. The image reverses, but in addition it glides. Instead of a mirror line, we have a glide line, or, a line that marks the path of a translation. Glide lines can run vertically, horizontally, or diagonally. Mirror reflection is a special case of glide reflection. Mirror reflection is glide reflection with zero glide, as translation is a special case of rotation. Thus, the four symmetry operations are reduced to two operations--rotation and glide reflection.

A symmetrical figure has repetative parts. The letters A B C are symmetrical through reflection. A mirror through the center leaves their appearance unaltered. A figure is symmetrical if a symmetry operation leaves the appearance unaltered.

N and Z are symmetrical by rotation. The word " bud " is symmetrical by mirror reflection. The word " pod " is symmetrical by rotation. The word " bobo " is symmetrical by translation.


A Succession of glide reflections establishes the akternate pattern of branching and leaf arrangements in this natural form.

Leaves on one side of the stem are mirror images of those on the other sede and each leaf grows in the gap between those that grow opposite.


 (Black/White part)

You will need a sheet of 8 1/2 by 11 transfer paper and two sheets of light weight Rives printing paper in addition to your other supplies.

STEP 1: Draw a 3 inch square on graph paper. Within the square make a simple asymmetric design of 5 to 8 pieces, with straight lines, curves or both. Make sure your design is asymmetric. Blocks that mirror symmetrically along a diagonal line are ones for which the symmetry is most often missed Check carefully for this. If you have trouble designing, you can hold a ruler high in the air, then drop it on the square. Draw a line where it lands. Repeat this process several times. Blocks with a solid bar down an outside edge tend to produce less exciting designs. If you have a bar, on the edge of your design, break it up or eliminate it. If you have lines drawn at odd angles, arrange them to begin and end on intersections of your graph paper. It will be easier to re-draw them in the next step of the process.

When your block is drawn you need to make a number of copies of it, all identical. Sixteen is a good minimum number to work with. For three inch blocks you will need more than one sheet of graph paper. You will also be making an identical number of mirror images.

Two methods for making reflections: 1 ) "You will be drawing 3" square blocks on the top sheet of the graph paper. Before you start to draw, lift up the top sheet and the second sheet of your pad and insert a piece of transfer paper, carbon side up, under the second sheet. As you draw on the top sheet, mirror blocks will come out on the back of the second sheet." Bear down hard. Mark A on the top of each block and B on the right side of each block before you rip the sheets off the pad. Cut the blocks apart. See sample "a". (This sample was done with 2 " blocks and then reduced for the copy). You will need more than one sheet of graph paper to do 3" blocks. In other words, you will use more graph paper designing the three inch block suggested first, but it will match the size of your printing block which must also be a 3" square. 2) Drawl 6 blocks edge to edge on one sheet. Mark the sides A and B. Have an acetate (clear plastic sheet) made on a copy machine. Have two copies made, on cardstock if possible, with the acetate first one surface up, then the other surface up. Use these blocks to experiment with rotation, reflection, translation and glide reflection. Thursday's exercise is one such pattern of rotation and reflection.

STEP 2: After experimenting with paper blocks and symmetry operations, choose a pattern that intrigues you. Transfer the design to a 3 inch block and carve it out. Remember to draw the design on the back of your block to avoid printing errors.

STEP 3: Experiment. Mix up a color and do test prints on white paper or newsprint to see how your pattern works in printing ink. PLAY. Try overlapping. You can cut small stamps out of the printing material to add extra shapes and colors for accent. Experiment with a few colors, and try using more than one color on your block. You can also make small patches with gouache to test out color combinations.

STEP 4: Make 2 final prints. See below

sample "a"

sample "b"

sample "c"

To turn in for homework:

1. On a sheet of heavy weight Rives paper: print your block pattern in two analogous colors. Each design from your block should have a minimum of 16 impressions. Four impressions across and four impressions down. Make sure to register your printing carefully to the edges of the paper so that your pattern is squared and centered neatly on the paper.

2. On a sheet of Rives paper: using the same block make a new pattern with the same number of impressions. Create the second pattern so that it looks completely different from the first pattern. Use two split complementary colors. How many different ways can you alter this pattern mathematically using the same block? Can you change the negative spaces. What happens when you change and shift the color with colors and values?

3. Glue the paper square pattern to another sheet of paper and bring it in for the crit

Remember that the paper is an off white. It represents a third color in its own right and will be the color of your negative shapes. Integrate all colors into the design to work with the symmetry of the pattern and please your aesthetic sense as well. You can simply alternate one color after the other in the printing process or choose a more complex sequence for the color. Optional: use a stamp to add more colors and shapes to the design. If you choose a pattern with reflections, you must carve a separate block to print the reflection of the original.

From Robert Henri: "THE ART SPIRIT"


THE possibilities of color are wonderful. A study entrancingly interesting and unliminted. It is a wise student who has a perfectly dean, well-kept palette -- glass over a warm white paper on a gootsizet table, always clean -- and uses such a palette to make continual essays with color-thousands of little notes, color combinations, juxtapositions of all the possible intensities of a well-selected spectrum palette. Many arusts just paint along, repeat over and over again the same phrases, little knowing the resources of the materials before them, and in many cases simply deadening their natural sense of color instead of developing it.

The backgrounds that are dark are very difficult to paint. That is, to make them seem like fine, breathable air. Of course it is easy to get away with a dark background, and it by its nature cannot be crude, but it can be heavy, snuffy, black.

The effect of brilliancy is to be obtained principally from the oppositions of cool colors with warm colors, and the oppositions of Brave colors with bright colors. If all the colors are bright there is no brightness.

However much you may use "broken color," hid on to the few simple larger masses of your composition, and value as most important the beauty and design of these larger masses, or forms, or movements. L)o not let beauty in the subdivisions destroy the beauty or the power of the major divisions.

Whatever you feel or think, your exact state at the exact moment of your brush touching the canvas is in some way registered in that stroke. If there is interesting or reasonable sequence in your thoughts and feelings, if there is order in your progressive states of being as the paint is applied, this will show, and nothing in the wodd can help it from showing.

p. 168
We realize that there is no one way of seeing a | thing no matter how simple that thing may be. Its planes, values, colors, all its characteristics are, as it were, shuffled before each new-comer arrives, and it is up to him to arrange them according to his understanding. Once when I was a young student I heard another student spoken of as "one who saw color beautifully." I was very much impressed by this. So one has not only to see color but he must see it beautifully, meaningly, constructively!-as a factor in the malting of something, a concept, something in his consciousness, something that is not exactly that thing before him which the school has said he should copy. This thing of seeing things. All kinds of seeing. Dead seeing. Live seeing. Things that are mere surfaces. Things that are filled with the wondrous. Yes, color must be seen beautifully, that is, meaningfully, ant used as a constructive agent, borrowed from nature, not copied, and used to build, used only for its building power, lest it will not be beautiful. It is very hard to see this aspect, our aspect, of the thing before us. It is very hard because it is the simplest thing we do. If you could catch yourself while on some ramble in the woods and know the source of your happiness, and continuing the same kind of seeing, proceed to paint, the work you would do would be eventually a revelation to you. Eventually, I say, for at first it would shock you, so different would it be from that convention which has enslaved you. It would be your original output. The easiest thing is the hardest. It is harder to be simple than it is to be complex. Schools of new vision rise and fall. The type of that man who said he couldn't see shadows purple but hoped soon to do so, is yet our average type. We are not yet developed to the plane where there are many who would pit their own originality against the fashion of the day. It is, however, to the artist or to the scientist- there are times when the distinction disappears- that we look for that freedom which will return us to simple understanding. Our future freedom rests in the hands of those whose likeness will be in their dissimilarity, and who will not be ashamed of their own originality, whatever the fashion may happen to be.

From Ocvirk, Otto G. :"Art Fundamentals"

Uses of Color  p. 116

Being familiar with the sources of color and its principal properties is of little value unless we can understand how these facts are used by the artist. Color serves several different purposes in artistic composition. These purposes, however, are not always separate and distinct; they frequently overlap and are interrelated. Color may be used in the following ways:

  • 1. To give spatial quality to the pictorial field
    • a. Color may supplement, or even substitute for, value differences to give plastic quality.
    • b. Color may create interest through the counterbalance of backward and forward movement in pictorial space.
  • 2. To create mood and symbolize ideas
  • 3. To serve as a vehicle for the expression of personal emotions and feelings
  • 4. To attract and direct attention as a means of giving organization to a composition
  • 5. To accomplish aesthetic appeal by a system of well-ordered color relationships
  • 6. To identify objects by describing the superficial facts of their appearance

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© Copyright 1996, Pippa Drew and Dorothy Wallace, Dartmouth College