Lesson4 Art Lecture

Lecture 4 Art Lecture

20th Century artists who use symmetry to explore color theory


We will be investigating two contemporary artists, Josef Albers and Sol Lewitt, who are often associated with Minimalist and Conceptual art. [note 1]   These artists have employed simple geometric forms and mathematical concepts in their endeavor to reveal the illusory effects of color on the two- dimensional plane.

Josef Albers, 1888-1976, German

The work of Josef Albers presaged the art of Minimalism and Conceptualism in the 1960s. In his earlier career, Albers was a major figure of The Bauhaus, an influential German school of design and architecture. The Bauhaus developed out of a movement called European Constructivism, a purely abstract, geometric style that emerged shortly before the 1920s. The Bauhaus Constructivists believed that pure abstract forms, such as lines, squares and triangles were more valid than representational painting. For these artists such pure forms evoked a "universal" reality. [note 2]   Albers eschewed representation, in favor of the abstract and hard-edged geometric shapes he employed in his most celebrated works. He said "... art should not represent, but present," and preferred the "anonymity of machine-like precision for personal expressiveness." [note 3]

From Werner Spies: "Albers"
Harry N. Abrams, Inc., New York
From the Homage to the Square series, p. 21

Homage to the Square, Interaction of Color
In the 1930s Albers emigrated to America from Europe, teaching at Black Mountain College in North Carolina. Later he taught at Yale University where he worked for 20 years on a series called "Homage to the Square." These paintings investigated the retinal effects of color. He published the fruits of this systematic research in a volume called, the Interaction of Color in 1963. Albers used nested squares to investigate color interaction. The simplicity of these designs revealed the way "abutting" colors could expand and contract, recede or advance, or even create a third color when only two were present. The varied use of scale and proportion also influenced the way certain colors interacted. [note 4]

From Werner Spies:"Albers"
Harry N. Abrams, Inc., New York
From the Homage to the Square series, p. 49

Because colors have powerful emotional associations, each combination of colored squares created a distinct psychological impact on the viewer. [note 5] While the squares he used to convey color interaction were simple, hard-edged geometric shapes, Albers saw his paintings as profoundly inventive and more expressive than a representational painting. "When you see how much color helps, hates, penetrates, touches, doesn't that parallel life?"

From Werner Spies: "Albers"
Harry N. Abrams, Inc., New York
From the Homage to the Square series, p. 51-57

Paintings from Homage to the Square are best experienced as a series. Albers is often considered the father of "series" art along with other late modern approaches such as Hard Edge, Minimal art, Op art and Conceptualism.

Sol Lewitt, (American, born 1928)

Class visit to see installation by Sol Lewitt at the Hood Museum of Dartmouth College
Sol LeWitt has been a leading avant garde artist in America since the 1950s. He is known both as a minimalist and a conceptualist who deals with multipart structures. A principle characteristic of conceptual art is that the "'true' work of art is not a physical object produced by the artist but consists of 'concepts' or 'ideas'..." [note 7]   Below is the verbal description and xsaccompanying images of Lewitt's wall drawing.

Verbal description of installation

Prints of Installation

Sol LeWtt
Wall Drawing # 655

The wall is divided vertically into three equal parts. The first and third parts are divided horizontally into fifteen equal parts; the second part is divided vertically into twelve equal parts. Each part with three-part combinations of color ink washes superimposed.

First Drawn by David Higginbotham
First Installation: Hood Museum of Art, Dartmouth College, Hanover NH, October 1990
Collection of the Artist
© Sol LeWitt

Sol LeWitt made the first of his "wall drawings" in 1968 for an exhibition at the Paula Cooper Gallery in New York, and they have formed an important part of his work since then. Comprised of webs of colored lines or, more recently, of pure geometric shapes such as cubes, pyramids and rectangles, they represent the artist's continuing interest in the mathematical analysis of form. A leading advocate of conceptual art, LeWitt conceived of his wall drawings as detailed sets of instructions that could be executed by an assistant. The hand of the artist is not necessary because, as LeWitt remarked, it is the idea that "becomes the machine that makes the art." The achievement of LeWitt's art lies in his perception of the expressive potential of rational structures. However austere in conception, his wall drawings are not simply analytic in character, but also mysterious, subtle, and sensual. [note 8]   (Hood Museum)


The Oxford Companion to Tentieth-Century Art
Edited by Harold Osborne. Oxford, New York, Oxford University Press, 1984.
p. 12

The Oxford Companion to Tentieth-Century Art
Edited by Harold Osborne. Oxford, New York, Oxford University Press, 1984.
p. 122

The Oxford Companion to Tentieth-Century Art
Edited by Harold Osborne. Oxford, New York, Oxford University Press, 1984.
p. 128

The Oxford Companion to Tentieth-Century Art
Edited by Harold Osborne. Oxford, New York, Oxford University Press, 1984.
p. 325

The Oxford Companion to Tentieth-Century Art
Edited by Harold Osborne. Oxford, New York, Oxford University Press, 1984.
p. 376

Daniel Wheeler: Art since mid-century: 1945 to the present
Imprint: Englewood Cliffs, N. J.: Prentice-Hall; New York: Vendome Press, 1991.

Daniel Wheeler: Art since mid-century: 1945 to the present
Imprint: Englewood Cliffs, N. J.: Prentice-Hall; New York: Vendome Press, 1991.

Minimal art taken up by the critic Barbara Rose in 1965: art works which [have] an unsually low degree of differentiation e.g. uniformly painted monochromatic canvases, and therefore a mimimal amount of 'art-work' on the part of the artist. Oxford Companion to 20th Century Art. p. 376.

How do these minimalist/conceptual works affect you? Do you value experiencing a work of art that rests on 'concept', rather than a physical essence?
How do these minimalist uses of form make us more aware of color?
In your opinion do the methods of these artists resemble a mathematical process?

Review of symmetry groups in pattern.

Amish Quilts
Albers and Sol Lewitt use very simple symmetries to explore color. Traditional textile patterns use color with more complex symmetries.

Observe the exploration of color interaction through the use of geometric shape in the quilting art of naive Amish artists.

From Rachel and Kenneth Pellman: "The World of Amish Quilts"
Good Books, Intercourse, Pennsylvania 17534, 1984

Fig 20, 21, 22, p.17

Fig 168, p.85

Contemporary Quilts


From the Studio of NANCY CROW, p.39

From RUTH B. McDOWELL: "SYMMETRY -- A Design System for Quiltmakers"

Musical Notation Quilt, p.91

Painted Daisies Quilt, p.92

Poppies Quilt, p.94

Trillium Quilt, p.106

Quilters have explored beyond the repetion of one symmetry group. together
Displaying p4, p4mm, p4gm, p3, p6 symmetries
Symmetry transforming to another symmetry
Symmetry interrupted and then moving back to former symmetry

What sorts of symmetries do you see here in Albers work, in quilting?
What impact could color have on your perception of a symmetry group?

construct a symmetry group with asymmetric motif

1. Create an asymmetric motif on your graph paper that measures approximately one to two inches wide and/or long.

2. Use your assigned symmetry group to put the motif in repeat on the graph paper. Experiment with the motif and the symmetry group using tracing paper so that it can repeat in an intriguing way.

3. Draw enough repeats to get a sense of the planar pattern -- about 8-12 repeats across and down on your graph paper. The amount of repeats needed will depend on both your motif and symmetry group. Try to complete as much as possible before the end of class.

Home work for 3- and 6-fold symmetry designs

Assignment 4 Part 1


Paint an effective pattern design using:
1) your assigned symmetry group exercise from today, and
2) colors demonstrating color interaction. Refer to the color interaction pages with this handout.

Paint an effective pattern design using: 1) your assigned symmetry group exercise from today, and 2) colors demonstrating color interaction. Refer to the color interaction pages with this handout.

From Benjamin Martinez, Jacqueline Block: "VISUAL FORCES

AN INTRODUCTION TO DESIGN" Prentice-Hall, Inc., 1988

Please read the following before beginning assignment 4

Color Interaction
P. 206-207

We have noted repeatedly that there is no such thing as a single and isolated color. Colors are always seen next to other colors. Even a colored dot on a sheet of paper will interact with the color of the paper-say, bright or dull white, buff, gray-and the two colors will change each other to some degree. When we speak of a color's hue, value, and intensity, we are describing that color in an imaginary void; when the color is placed in a context of surrounding colors, everything is changed.

We have seen how a gray appears to change dramatically when we alter the value of the field upon which it sits (Fig. A on page 172). An even more complicated pattern of interactions exists for color, with its many properties. The hue, value, intensity, and temperature of a color area are all affected by color interaction. In Fig. A a single, fairly neutral color is placed in four different color fields, and it changes its guise each time. Color interaction can make a single color appear hotter, cooler, lighter, darker, redder or bluer than it is. These color changes occur whether we want them to or not, so it is critical for artists and designers to understand just how colors interact and to anticipate those interactions. It is frustrating (and sometimes expensive) to mix a perfect tone for a particular purpose only to discover that it becomes a different color when applied to a white canvas or illegible when printed on green paper. The Italian Renaissance painter Titian must have recognized the importance of knowing how to manipulate the appearance of color when he bragged, as he supposedly did, that he could use mud to paint the flesh of Venus. What he meant was that if he could get a muddy, low intensity color into the right relationship with surrounding values and colors, it would appear luminous, brilliant, and rich.

Probably the best-known systematic investigation of color interaction is found in the series of paintings by Josef Albers called "Homage to the Square." Albers chose the square as the most neutral format, neither too high nor too wide. He did not mix colors for these paintings, but used them straight from the paint tube, applying them smoothly and evenly and making sure that no blank strip separated one color from another. There are no complex compositions in the series, and the square format of the outside is echoed within. Still, there is plenty to look at and work with. The size of the interior squares, the widths of the bands they create, and the hue, value, intensity, and temperature differences resulted in distinct and varied color personalities and kinds of light from one painting to another. A painting based on variations of orange might glow like a kiln. The opposition of blue and white might create the open and airy feeling of a Mediterranean landscape. Color might be made to feel compressed or expansive, edges made to seem crisp or dissolved (Figs. B and C).


Figure B. Josef Albers, "Homage to the Square: Silent Hall." 1961. (Collection, The Museum of Modern Art, New York; Dr. and Mrs. Frank Stanton Fund)

Figure C. Josef Albers, "Homage to the Square: Apparition." 1959. (Collection, Solomon R. Guggenheim Museum, New York)

Color Interaction: Simultaneous Contrast
P. 208-209

We have already noted the effect of afterimage, the ghostly image of a color's complement that one sees after staring at a color spot. When we look at colors that are next to one another, something similar happens. A black dot placed on a red field will look greenish, and placed on a green field it will look reddish (Fig. A). The color of the field (say, red) will "call forth" its opposite quality (green) in a black dot placed upon it. This is something that happens in your eye and not on the page; if you peeled off the black dots, they would still be black. If you wanted the black dot to look black on a red field, you would most likely have to make it a very dark red to compensate for the ghostly aura of green.

We call this effect in adjacent colors simultaneous contrast. The principle applies to all such interactions. A color will appear darker in value on a light ground and lighter on a dark ground, more intense on a more neutral ground and grayer on a very intense ground (Fig. B). Green will look more yellow on a field of blue and more blue on a field of yellow (Fig. C).

The effect, furthermore, is modified or enhanced by the particular colors chosen. Pure, intense, primary hues are not much affected by context, but lower-intensity colors and colors that are not primary or spectral can change appearance radically.

Size can also influence the effect of simultaneous contrast. Generally, larger color areas have more influence on smaller color areas. The small green square is changed by the color of the yellow or blue field, not the reverse. This is why colored type seems to be affected by the color of the ground and not the reverse, or why a red thread running through a green cloth looks so brilliantly red. Although we are usually not conscious of this "optical illusion," it is something we continuously experience in our ordinary perception of things. We do not see it happen unless it is presented in diagramatic form as in the figures here. The effect of simultaneous contrast is only interesting to the viewer of a work of art or design, but absolutely critical to its maker.

Part Two of Art Lecture 4

Exploration of color interaction and symmetry through the work of an Op artist


1) to become familiar with Op art.
2) to explore the use of pattern and color in the work of Op artist Vasarely
3) to observe how altering a symmetry impacts a pattern visually

Victor Vasarely, Hungarian-French 1908.

As a young artist in 1928, Victor Vasarely studied at the Bauhaus school in Budapest, fully identifying with the geometric Constructivist style. [note 1] He emigrated to France in the 1930s, and in the 1950s, became a leader in the European Op art movement. Op artists contrasted saturated colors or black and white to create optical illusions that vibrated with after-images. [note 2]   They explored the motion and energy of optical effects with the same degree of thoroughness that Albers had investigated color. [note 3, note 4]   While these vibrating designs gained avid media attention in the US, American critics were slow to admit Op art into their canon of "High Art". [note 5]   However, in France, European Constructivism permeated many art movements because of its social idealism. Op artists such as Vasarely saw optical art as an egalitarian tool for the 20th Century. [note 6]

From Gaston Diehl: "VASARELY"

Eridan-III 1956 Oil
Detroit Institute of Arts

In his early work Vasarely experimented with the tromp d'oeil effects of such subjects as zebras and checker boards. [note 7]

He moved on to develop "plastique cinetique" or "mathematically controlled [abstract] forms and colors" that he endlessly arranged and rearranged into diverse patterns. [note 8]

From Gaston Diehl: "VASARELY"

Vega-II 1957-59 Oil
Tel-Aviv Museum

Vasarely used circular, oval, triangular, or square shapes in complex grids to create powerful optical pieces. When a shape deviates from the pattern, it produces a sense of movement, receding and advancing from the picture plane. Graduating values create a smooth progression across the plane, while complementary colors form abrupt shifts. [note 9]

From Gaston Diehl: "VASARELY"

Zett, 1966 Vinyl

Museum of Contemporary Art, Montreal

Vasarely referred to these geometric modules, and the infinite variety of patterns they created, as "planetary folklore." He envisioned that technology itself would disseminate this art form, rather than individual artists. Units of abstract shapes and colors alone would create uplifting environments for mankind. In this way, Vasarely sees geometric abstraction as a democratic influence "free of psychological associations."

From Gaston Diehl: "VASARELY"

Museum of Contemporary Art, Montreal

Vega-JG, 1967 Vinyl
Collection James H. Clark, New York

How is the work of Vaserely similar to the work of Albers?
How is it different?
What kinds of symmetries does Vaserely use?
How does color affect the symmetries here? What else happens to the symmetries?
What is your response to Vasarely's system of shapes and colors (planetary folklore)?

The rest of this class is spent on sketches for homework, Assignment 4.

Assignment 4 Part 2

Create a composition in gouache by repeating and then interrupting a symmetry group. You will be working to achieve spatial relationships in your design. When you dissolve, break or change a symmetry group, you establish movement away from and toward the picture plane. Since uninterrupted repeating pattern accentuates flatness, disruption creates depth. You will also apply color gradation and color interaction to create space, volume and movement. This assignment is modeled on Vasarely's paintings. Don't hesitate to use short-cuts such as tracing paper and a Xerox machine, to reduce your labor on the project.

Shibori - A Definition

 Lesson 1 | Math partArt part |
 Lesson 2 | Math partArt part |
 Lesson 3 | Math partArt part |
 Lesson 4 | Math part