Shape. Mathmatics. Art.

The intersections of what we think of as different fields of study fascinates me. These videos I stumbled across today provide some tantilizing connective tissue between art and mathematics in the work and research of Eric Demaine. What I liked best was Eric's statement that mathematics is an art medium. And his, sometimes a bit rattled, SEED presentation (Scroll down to see the embedded video) proves that he is working from the spirit that drives all of us who make art.

First, here are the links to an animation of the Metamophosis of the Cube

The background of the animation of
Metamophosis of the Cube even has its own little artfull story:

Watching the animation, you'll probably notice the old page of cyrillic text in the background. There are a couple of reasons for this. First, it gives something onto which the folding objects can cast shadows. Second, it is in some sense the basis for our work. The page is from a Russian book on Convex Polyhedra by the famous Russian geometer A. D. Aleksandrov. In particular, the theorem underneath the folding cube characterizes what “polyhedral metrics” can be folded into convex polyhedra.

The Shape of the Matter

I've been playing around with notan expanded squares for years, ever since Jane Dunnewold of Art Cloth Studios showed our class the Japanese exercise. Her explaination is on the tutorial section of the Art Cloth Studios website, so you can go there and get the instructions straight from my source.

As Jane writes, so eloquently (as she always does),

Both symmetrical (the same all around) and asymmetrical (different on each side) designs can be achieved through the use of the expanded square concept. In order for the exercise to be completed successfully, there must be a feeling of balance in the design created. A symmetrical design can still be heavy, ponderous, or boring. If the design is working, it will be interesting and will feel balanced on all four sides. Test this idea by turning your paper as you study a completed design. Does it measure up when rotated and studied? Is it interesting from all directions?

There are many other notan exercises, all of them derived from what is considered a kind of visual meditation sometimes by its practitioners.This example is even simpler in execution. Simply cut a square apart in any way you wish, with the object being to reassemble it with white space in between, making again a pleasing and intriguing balance of white and black, light and dark.

I also like to play with the shapes in multiples, enlarging and reducing them on the copier, then reassembling into a rhythmic shape composition.

These exercises are a neverending source of inspiration for stamps, whole cloth quilts, applique, stencils, screen-printing and other graphic applications to fiber arts. I'd love to see your examples! Like snowflakes, there never seem to be two alike! Here's another site with examples too, from Princeton Online.

And here's a wonderful extension of the discipline into maskmaking by a class at San Jose.

By the way, there is room for one more shape-minded person in June's The Shape of the Matter workshop at El Cielo Studio. We'll be doing notan and lot's of other shape exercises in design, using shape as the structural bones for an art quilt, and more. If you're interested, send me a message via the contact box on the sidebar. Dates are June 26 - 28. For further info, see the workshop page.

And, if you're not overwhelmed with opportunities yet, you can find more shape exercises in our new book -- yes, it's for parents, but each set of activities includes a page for the grownup investigators, too.
Here's the exercises in the Shape section -- plus a whole slew of others that didn't make it into the book. I'd love to hear your ideas, too.

Shape investigations to do on your own:

Explore your home as though it were a museum. What kinds of shapes have you collected, consciously or unconsciously? Make an arrangement of disparate objects that share a shapely characteristic on a bookshelf or windowsill. What would the catalog of these shapes say about you?

As you drive through your neighborhood notice the shapes of buildings, homes, stores and other structures. Do the shapes that you see serve as clues to architectural eras, the history of the street? If yours is a new neighborhood, what historical styles have the builders called upon for inspiration? Shapes of windows, doors, rooflines and facades are your best clues.

Cut or tear shapes from colored paper and collage them to solid colored cards for interesting personal note paper.

Enroll in a ceramics class at a local art center or continuing education department of a local college or university. Or for self-guided exploration buy a 50-pound box of ceramic sculpture clay from a local supplier.

Watch a dance or mime performance (live or recorded) with an eye for shape, how the performers use their bodies and each other to create shapes in space. Some troupes and artists to look for: Mummenschanz (on the web at www.mummenschanz.com), Martha Graham -- who else?


Take a walk along a creek bed or river and visually collect the shapes you see in stones and water.

Dip into Georges Perec’s 1978 Life A User’s Manual, a non-linear novel that uses writing constraints – rules that the writer has imposed on the content and structure of the book – much in the way a visual artist uses shape in the composition of a painting.

Write a haiku each morning for a week about the weather outside your window. (How do constraints of syllable count shape your thoughts?)

Think about how your clothing affects your silhouette as you dress for work or play. Make an effort to wear something that changes your shape and pay attention to its effect.

Collect a specific shape (circles or cones, for example) or specifically shaped objects (manholes, terracotta vases, interesting doors) by photographing throughout a day, a week, a month. Post your collection on a photography website, such as Flickr, to share it with others.

Carve simple shapes using a craft knife into the side of an art gum or white artist’s eraser. Make shape patterns and grids using black stamp pad ink on white paper. Enlarge and reduce and repeat shape patterns using a copier. Can these inspire a quilt or other art project?

Finding Your Voice, Your Path

We all want our work to be distintive and unique. Really, don't we? No matter how much we admire the work we see of other artists, when we embark on the journey of living the artist's life, we want our work to sing with our own voice. I think there are several parts to finding that voice, that path (if voice in a visual sense seems too mixed a metaphor). I also think the process is similar no matter your medium and whatever the field you pursue, be it art, quiltmaking, physics or cookery. As I've been teaching this past week, and heading into two more workshops this week -- one in Austin for the Austin Fiber Artists and my own recurring Artist Journal/Artist Journey retreat this weekend -- this piece I wrote a couple of years ago -- and revised for the upcoming events -- bears repeating. Today, Part One:

Think about "Pure Form:"

I believe – and my belief is supported by more than 30 years of work with children in creative learning environments – that each of us is born with an innate preference/leaning toward a particular way of perceiving and giving form that is directly connected to what I (and my colleagues in this work) call the Sensory Alphabet. This vocabulary of non-verbal qualities – line, color, shape, space, light, texture, movement, sound and rhythm -- is a way of thinking about and organizing one’s individual strengths of perception and invention. Looking at one’s preferences and natural tendencies through this lens serves as both a way to self discovery and as a bridge to understand other creative work. This vocabulary is not just an artistic one – it can hold as true to creative work in business as in design, in science as in art.

If you think about letters of the alphabet as being the building blocks of literacy (both spoken and read and write) and numbers as the building blocks of mathmatics and physics, then the Sensory Alphabet is what can be a symbol system for everything else (and even math and words, sinces it's more primal, more connected to our bodies and minds in a very basic way.)

Think about which of these constructs is easiest for you to notice, to manipulate, to play with –is it pattern (rhythm) or texture or color? What did you love as a young child? Which of these elements are most important to you in your home, your environment? What artists do you resonate to? Design exercises and experiences for yourself that feed your mind’s natural interests, or find teachers that share your sensibilities (look at their work and see what they say about it) who can provide classes that feed your perceptual strengths.

An understanding of your own creative style in terms of this vocabulary can be the starting place for finding your voice – and even help you find the best and strongest medium for work. For example, if color is my strong suite, I might take time to do dye and discharge samples, study Albers and other colorist’s work, take photos exploring color themes, investigate watercolor and glazing, look at color as understood by chemists and physicists, etc. If movement is a strong suite, I might see how to incorporate moving elements in my textile work, take up techniques that use my body in strenuous and challenging fashion, look at how movement blurs an image and how to capture that sense with dyeing or printing, I might even want to dye fabrics and construct garments for dance performances or architectural installations with moving components.

Most of us have three or four of these strong suites that interact in interesting ways and can pose intriguing puzzles for our work. Tracking down your strongest perceptual elements is usually just a matter of paying attention to preference, to what you notice in a space, to the materials that call your name. Journaling about childhood preferences and doing detective work in your closet, your home, your memory bank can help you name your sensory strengths.

Our book, New World Kids, The Parent's Guide to Creative Thinking includes investigations and invention activities for adults as well as for adults and children, despite the title. We think parents need to nurture their own experience with this alphabet in order to recognize their children's strengths and learning styles. Here's an example for TEXTURE -- since most of us who end up in the fiber arts are almost certainly drawing on some interest and facility for texture, I figure it might spur you own with some Sensory Alphabet play!

From NEW WORLD KIDS, all rights reserved.

TEXTURE investigations to do on your own:

1. Examine your wardrobe and make a texture inventory.
What textures really suit you? What feels good against your
skin? Make a point to buy something with a pleasing texture
the next time you shop.
2. Cook a meal with a conscious plan to include contrasting
textures, as the Japanese do. Do certain kinds of tastes correspond
to certain kinds of textures? Think temperature as well
as crisp, creamy, grainy, smooth.
3. Where can you experience coarse, slimy, mushy, matted,
abrasive, elastic, sleazy, itchy, silky, downy, frothy, fuzzy?
Consciously create one new tactile experience each day for a
week.
4. Listen to different music with an ear toward texture: contemporary
jazz, baroque, chant and heavy metal are a few contrasting
genres to try.
5. Visit a museum’s textile or fiber arts exhibitions or explore
some online exhibitions or galleries. Try one or more
of these key words for a search: fashion, art quilts, traditional
quilts, art cloth, knitting, weaving, wearable art, basketry, fiber
arts, shibori, batik.
6. Study and write a poem about the textures of your body,
inside and out.