One Motif, Four Moves

The idea: pattern

Pattern is the repetition of a motif, such as a shape, line or color, in a planned and regular arrangement across a surface. A motif can repeat by sliding, turning, mirroring, or mirroring and sliding at once.

In a notan: A notan is patterned from the first cut: every shape repeats once, as its mirrored piece, in the opposite value. Repeat the cut and the pattern doubles. A row of holes along an edge makes a row of pieces beyond it, the second row a mirror of the first and reversed in value, so a border in the sheet becomes a border on the ground. The four ways a motif can repeat across a flat surface, sliding (translation), turning (rotation), mirroring (reflection) and mirroring while sliding (glide reflection), are all in the studio’s Transform and Copies. The fold is one more reflection laid over whatever you build: any pattern that folds out across an edge is repeated again, mirrored, on the other side.

A pattern is a motif and a rule for repeating it. On a flat surface there are only four basic moves: slide the motif along, turn it about a point, mirror it across a line, or mirror it and slide it at once, the glide that turns a left footprint into the next right one. Every wallpaper, tiled floor and printed fabric is built from these four. In 1891 the crystallographer Evgraf Fedorov proved that they combine in exactly seventeen distinct ways to repeat a pattern in two directions across a plane.

Notan adds a twist. The fold is a reflection too, so any pattern you cut near an edge repeats once more beyond it, mirrored and in the opposite value. In this activity you build each of the four moves from one asymmetric motif, predict how each survives the fold, and then combine them into a single design. Last, you cut the motif as a stencil, print it by hand, and set the prints beside the same motif cut and folded.

Art history

Pattern-makers have explored these moves for centuries, and every work below was made by cutting: cut tile, cut paper, carved printing blocks and a woodcut. Each makes one or more of the four moves easy to see, and one of them already behaves like a notan, with dark and light shapes that are each other’s spaces.

• Nasrid craftsmen Tile mosaic dado, Hall of the Ambassadors, Comares Palace, c. 1333–54 Alhambra, Granada

  The lower walls of this throne room are covered in alicatado, glazed tile cut into small pieces and fitted into interlacing star patterns. Look for the turns around each star and the mirror lines running through it. M. C. Escher spent days copying the Alhambra’s tilings in 1936, and they set the direction of his later work.

• Anonymous Japanese artisan Textile Stencil (katagami) with Chrysanthemum Design, 1800s–early 1900s Harvard Art Museums, Cambridge, Massachusetts

  Katagami are paper stencils, cut from mulberry paper toughened with persimmon tannin, through which a resist paste was spread onto cloth before dyeing. The stencil was laid down again and again along a bolt of fabric, so one cut sheet produced an unbroken repeat: a slide, made by hand.

• William Morris Strawberry Thief, 1883 Victoria and Albert Museum, London

  Morris based this printed furnishing fabric on the thrushes that stole strawberries from his garden. It is a turnover, or mirror, repeat: pairs of birds face each other across a vertical axis, and the whole unit then slides to repeat across the cloth. Two of the four moves, working together.

• M. C. Escher Day and Night, 1938

  A checkerboard of fields rises into interlocking birds: black birds flying one way into daylight and white birds flying the other way into night, over a landscape mirrored from left to right. It is a tessellation and a notan at once, since each flock is shaped by the spaces between the other.

Design today

Pattern designers think in repeats. A textile or wallpaper design is drawn as one tile that must join itself seamlessly on every side, and the tile is then set out as a straight repeat, a half-drop, in which each column is shifted down by half a tile, or a mirror repeat like Morris’s. Maija Isola’s Unikko poppy print for Marimekko, from 1964, is still in production, and its huge flowers show how much the scale of a motif changes the feel of a repeat.

Brands use pattern as identity. The Louis Vuitton Monogram canvas, launched by Georges Vuitton in 1896, repeats initials, flowers and quatrefoils so that the pattern itself becomes the signature; it was designed partly to make the luggage harder to counterfeit. One habit carries over: before you commit to a pattern, look at its seams. In a wallpaper it is where one tile meets the next. In a notan it is the edge of the sheet, where every pattern meets its own reflection.

Warm-up

Fold and cut. Fold a paper strip back and forth like a fan into six or eight panels. Draw a simple motif on the top panel that touches both folded sides, cut it out through every layer, and open the strip. Each figure is a mirror image of its neighbor: folding has made a mirror repeat, the move Morris used in Strawberry Thief. Notice that each fold does what the edge of a notan sheet does.

In the studio

Make it in Studio Notan, where every cut can be moved, refolded and undone.

1. Design an asymmetric motif. In the studio, use the Pen to draw a small motif about half an inch across: a leaf with a hooked tip, a flag, or a letter such as F or R. It must look different when turned or mirrored, or the moves you are about to make will be invisible. Draw it near the top edge and fold it up.
2. Slide. Select the motif with Move. In ‘Transform’ on the Controls tab, set the Move ‘Horizontal’ to a little more than the motif’s width and ‘Copies’ to 5. Before you press ‘Apply’, turn ‘Preview’ off and sketch where you expect the new pieces to land; then turn it on again to check, and apply. The pieces above the sheet form a second row, each a mirror of its hole. One move in the sheet has made two patterns (see Copies).
3. Mirror. Draw a second motif near the bottom edge, fold it down, and select it with Move. Turn on ‘Reflect Y’, set the Move ‘Horizontal’ to about one motif’s width, set ‘Copies’ to 1 and apply: the copy lands beside the original as its mirror image, a turnover pair like Morris’s birds. The copy joins the selection, so now set a plain horizontal move of two motif widths with ‘Copies’ at 3 to slide the pair into a mirror border. (Keep ‘Copies’ at 1 for the pair itself: with a reflection and a move, every second copy lands back on the original.)
4. Glide. Draw a third motif near the left edge, fold it left, and select it with Move. Turn on ‘Reflect Y’ again, but this time set a Move ‘Vertical’ a little more than the motif’s height, with ‘Copies’ at 5. Because the reflection is across the line you are moving along, the copies alternate like footprints walking down the edge: a glide reflection.
5. Turn. Draw a fourth motif in the middle of the sheet, fold it right, and select it with Move. In the reference-point grid of nine squares, click one corner, then set the ‘Angle’ to 45 and ‘Copies’ to 7. The eight motifs fan around that corner into a rosette: a rotation. Beyond the right edge, the rosette’s pieces spin the other way, because a mirror reverses the direction of every turn.
6. Read the fold. Compare each pattern with its pieces. A slide stays a slide, a mirror border stays a mirror border, and a glide stays a glide, but each is reversed in value and mirrored across its edge. Check the seams: where does each pattern meet its reflection, and does the join look planned or accidental?
7. Loosen one pattern. Undo would take back everything since the top row, so instead click one of its five copies, Shift-click the other four, and press Delete. Select the first motif, turn on ‘Random’ in ‘Transform’, enter the same slide again, and apply it. Each step now takes a random share of the move, so the regular row becomes an irregular one, more like leaves on a path than tiles on a floor. Decide whether your design wants the exact version or the loose one.

With paper and paint: Print through the hole

Copies repeats a motif perfectly and at once. By hand, every repeat is its own act: lay the stencil down, dab, lift, move it one step, and again. That rhythm is how the patterns in this lesson were made. A katagami stencil, made strong and water-resistant with persimmon tannin, was laid down again and again along a bolt of cloth, and Strawberry Thief was printed from carved blocks, one impression at a time. Paint shows the hand in every print, a little heavier here and lighter there, so you see how much variation a pattern can hold and still read as regular. And a cut stencil gives you both halves of a notan at once: the hole prints the motif dark on light, and the piece, used as a mask, prints it light on dark.

1. Cut the stencil. Cut a square of cardstock as tall as your strips, about 4 inches. Draw your studio motif about an inch and a half tall, centered from side to side and a little above the middle: the hooked leaf, the flag or the F. Keep it one solid shape with no enclosed hole, since the loop inside an R would fall out of a stencil unless you left a narrow bridge to hold it. Cut it out on the mat and keep both halves: the square with its hole is the stencil, and the cut-out motif is the piece.
2. Print a slide. Along both long edges of each strip, mark five points two inches apart, starting an inch and a half from one end, and draw a short tick at the middle of the stencil’s top edge. Load the stencil brush with a little paint and dab most of it off on a paper towel until the brush is nearly dry. Set the stencil flush with the strip, its tick on the first mark, hold it flat, and pounce straight down through the hole; brushing sideways pushes paint under the edge. Lift the stencil straight up. Print the first, third and fifth marks, then fill in the second and fourth once those prints are dry, so the stencil never lies on wet paint.
3. Print a mirror border. On a second strip, print the first, third and fifth marks with the stencil face up. When the prints and the stencil are dry, turn the stencil over like the page of a book, so the tick stays at the top, and print the second and fourth. Each print is now the mirror image of its neighbors: a turnover repeat like the facing birds in Strawberry Thief, sliding along as a border.
4. Print a glide. On a third strip, print the same way, but for the in-between prints turn the stencil over from top to bottom, like a calendar page, and line its tick up with the marks along the lower edge. Because the motif sits a little above the middle of the stencil, the turned prints fall below it, and the strip walks like a row of footprints.
5. Print around the piece. On the last strip, lay the cut-out piece face down, so it is mirrored like a folded notan piece, and hold it in place with a small loop of tape underneath. Pounce paint over its edges onto the paper around it, then lift it: the motif stays white inside a halo of paint. Repeat at each mark. The hole printed the motif dark on light; the piece prints it light on dark. One cut has made both values, as in a notan.
6. Cut the same row. Trim black construction paper to about 11 by 5 inches and mark the same five points along one long edge. Set the stencil’s top edge along that edge, line its tick up with each mark, and trace inside the hole with the white pencil, so every cut matches the prints. Cut out the five motifs. Glue the sheet along the bottom of a sheet of white cardstock turned sideways, then turn each piece over across the top edge, like a calendar page, and glue it as far above the edge as its hole sits below it.
7. Compare the repeats. Pin the printed strips beside the cut row and step back. A printed slide shows the motif once at each step; the cut row shows it twice, as a hole and as a mirrored piece in the opposite value, so one row of cuts makes two rows of pattern. The prints carry the stippled texture of the brush and small differences from one print to the next; the cuts are flat and exact. Which reads more strongly as a pattern from across the room, and where does each repeat meet its seam?

Take care: Cut on a self-healing mat with the blade moving away from your body and your other hand behind it, and let an adult handle the knife for young learners. Use paints labeled non-toxic (look for the ACMI AP seal), cover the table, let prints dry before the stencil touches them, and wash the stencil brush in soapy water straight away, since acrylic left to dry ruins the bristles.

Take it further

Try Escher’s method for a shape that tiles. Draw a square with Rectangle, then use Points to push a bump out of its left side and pull the same curve, as exactly as you can, into its right side, so that what leaves one side arrives at the other; do the same for the top and bottom. The arrow keys nudge anchors by exact steps, which helps the two curves match. Step it with Copies exactly one tile width and the tiles lock together, with gaps only where the curves differ. Step it two widths instead, so that only every second tile is cut, and the paper left standing between the holes takes the holes’ own outline on each side. Figure and ground begin to trade places, the effect Escher pursued in Day and Night.

Reflect

• Which of the four moves was easiest to see, on screen or in print, and which was hardest to spot?
• How did the fold change each pattern, and why did the rosette’s pieces spin the other way?
• Where does your pattern meet its own reflection at the edge, and does the join look planned?
• Which historical pattern uses a move you did not expect, and where?

What to look for

• The motif is asymmetric, so turns and mirrors are visible on screen and in print.
• Each of the four moves is built with Transform and Copies using exact settings, with rows parallel to their edges.
• The stenciled prints have clean edges with no paint crept under the stencil, sit on even steps, and form a true mirror border and a true glide.
• The learner predicts, before the preview, where a row’s pieces will land beyond the edge.
• The learner names the moves in a partner’s design correctly.