Difference by Degrees

The idea: variety

Variety is the use of differences, such as changes in size, shape, direction, color or value, to create visual interest. It works with unity: too little variety is monotonous, and too much is chaotic.

In a notan: Variety in a notan is difference with a family resemblance. Because every piece repeats its hole, a notan has sameness built in; variety comes from what the designer chooses to change: the size of one cut against another, its angle, its outline, the spacing, and which edge each piece folds over. The colors add one more lever, since pieces show the back and holes show the ground. The discipline is to change one quality at a time and keep the rest, so every difference reads as a decision. Change everything at once and the mirror logic that makes a notan legible is lost in noise.

Variety is difference used on purpose. Without it a design is monotonous: the eye takes in the pattern at a glance and moves on. With too much, the design is chaotic: nothing relates, and the eye has nowhere to rest. Good variety sits between the two, and it depends on unity to work, because a difference only reads as a difference against something that stays the same.

A notan makes this easy to test. You can start with a row of identical cuts and change one quality at a time: size, outline, angle, spacing, the edge a piece folds over, the colors. After each change you ask whether the design became more interesting or only busier. The studio’s Undo lets you walk back to the exact step where it went too far. With paint and paper there is no Undo, so you plan the steps and test them with loose pieces before any glue.

Art history

Artists have long tested how much difference a work can hold. These four works run from a screen where a few repeated clusters are varied with great restraint, to a collage that courts chaos on purpose.

• Ogata Kōrin Irises, c. 1701–05 Nezu Museum, Tokyo

  Across a pair of six-panel folding screens, clumps of blue irises and green leaves cross a gold ground. Some clusters are so alike that scholars think Kōrin repeated them from a pattern, as a textile dyer repeats a stencil. The variety lies in how he spaces and groups them. Three colors, one flower, constant difference.

• Hannah Höch Cut with the Kitchen Knife Dada through the Last Weimar Beer-Belly Cultural Epoch of Germany, 1919 Nationalgalerie, Staatliche Museen zu Berlin

  Höch cut photographs and words from magazines and newspapers and packed them together: faces, machines, crowds and letters at every scale and angle. The variety is pushed almost to chaos, on purpose, to answer a society in upheaval after the First World War. Ask what keeps it from dissolving into noise.

• Romare Bearden The Block, 1971 The Metropolitan Museum of Art, New York

  Six panels of cut and pasted paper, photographs and paint make one Harlem street: a church, a barbershop, a grocery and the lives inside them. Every panel is crowded with different scenes, yet the line of the street and the run of facades bind them into one block. It is variety within unity, built from cut paper.

• Mary Lee Bendolph “Housetop” variation, 1998 The Phillips Collection, Washington

  Housetop quilts, a favorite pattern of the quilters of Gee’s Bend, Alabama, build frames of fabric strips around a central square. Bendolph made this one partly from polyester suits a relative had sent from Connecticut. Look for what the shared pattern keeps, the nested frames, and what each quilter is free to vary: the variation is in the title.

Design today

Editors plan variety deliberately. A magazine’s flatplan, the map of every page in an issue, is used to pace it: a full-bleed photograph, then a dense page of text, then a spread built on one word set huge. The typefaces, grid and colors stay fixed; variety comes from scale, cropping and density, so each turn of the page is a change without being a stranger.

In data visualization, variety carries meaning, so it has to be rationed. A good chart varies only what encodes data, such as a bar’s length or a point’s position, and holds everything else steady. Edward Tufte’s small multiples, the same small chart repeated in a grid with different data, are variety within unity at its most useful: because the frame never changes, every difference the eye finds is real.

Warm-up

Twenty ways to change a square. In five minutes, sketch as many variations of a small square as you can: bigger, smaller, turned, stretched, notched, rounded, doubled, split. Then circle the three that still read as squares and cross out the three that have left the family. The line between the circled and the crossed-out is the line this lesson walks.

In the studio

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

1. Open the studio. Draw a small circle near the top edge with the Ellipse (Shift, once dragging) and fold it up with ↑. Select it with Move, and in Transform set a horizontal move of about one and a half circle widths and 4 Copies. Apply. Five identical cuts: pure unity, and a little dull. Save the project from File and export a PNG as your “before”.
2. Size. Select the second circle alone and scale it to 60 percent in Transform. Select one circle at a time: Transform scales about the center of the whole selection, so scaling two together would also pull them toward each other. Look at the row. Did one change make it livelier, or only uneven?
3. Outline. Choose Points, Option-click the top anchor of the third circle to make it a sharp corner, then drag that anchor upward: the circle becomes a teardrop. Its piece changes to match, mirrored across the edge. The shape changes; the family survives.
4. Direction. Select the fifth circle with Move and click the arrow beside the bottom of its selection box. The piece folds back into its hole and out over the bottom edge instead. Notice how far one change of direction travels across the design.
5. Chance. Select the teardrop. In Transform set Scale to 70, Rotate to 45, a small move and 4 copies, then turn on Random. Each step now takes a random share of the scale, move and angle, and the preview shows exactly what Apply will make. Turn Random off and on for a fresh draw, and apply only a draw in which every child still looks like its parent.
6. Too far. Keep adding differences, new sizes, angles and fold edges, until the design stops holding together. Then press Undo one step at a time. The studio keeps the last fifty steps, so you can walk back and forward with Redo until you find the change that tipped it. Write that change down.
7. Color. On the Color tab, drag the Back swatch onto the Ground card to swap them. The pieces and holes trade colors. Does the difference between back and ground add useful variety, or noise? Swap back if it was noise. See Colors.
8. Export a PNG of the final design and set it beside your “before”. List every difference between them and say what each one is for. Any difference you cannot justify is a candidate for Undo.

With paper and paint: Paint by degrees, arrange on a grid

The studio keeps fifty steps of Undo. Paint and paper keep none: a mixed value stays mixed and a cut stays cut. So variety by hand has to be planned. You decide the steps before the brush touches the paper, and you try every arrangement with loose pieces before any glue. Painting the steps yourself also shows how hard an even step is. Equal measures of white rarely give equal steps of lightness, so your eye, not the spoon, has the last word. The Housetop quilts of Gee’s Bend keep one pattern, frames around a central square, while each quilter varies the fabrics. Here the grid and the parent shape stay fixed, and the paint and the cuts vary.

1. Set two dials and leave everything else alone. The paint will vary only in value: three steps of one color. The cuts will vary only in size: one square cut at three sizes. The paper, the brush, the shape and the fold stay the same. If you would rather vary texture, keep one mix and change only the brushwork: smooth, with visible strokes, then stippled, each covering the paper completely so the value does not change.
2. Paint the values. Paint the first piece of paper with the color straight from the tube or bottle. Mix the second value from one measure of color and one of white, and the third from one measure of color and three of white. Brush every sheet the same way, in two thin coats. When they are dry, lay them side by side and squint. If one step looks much bigger than the other, mix again and repaint the middle sheet: equal measures rarely make equal steps, and your eye is the judge.
3. Rule the grid. On the black ground, rule a grid of 4-inch squares with the white pencil, three across and three down. The grid is the unity that will hold every difference in place.
4. Cut the blocks. From each painted sheet, cut three 2-inch squares: nine blocks, three of each value. Cut with the knife against the metal ruler, or with scissors along a ruled line.
5. Cut by degrees. On the white back of each block, draw a square touching one edge: 1/2 inch on one block of each value, for the first row, 3/4 inch on the next three and 1 inch on the last three. Cut each square free, turn the block painted side up, and turn the square over its edge like a page, so it lands white side up, touching the edge where its hole does.
6. Arrange before you glue. Set the blocks on the grid, one in the middle of each square, each with its piece: values stepping lighter from left to right, cuts stepping larger from top to bottom. This is variety held in unity, like a page of small multiples: one grid, one parent shape, two dials turned one step at a time.
7. Now turn the dials too far, with loose pieces. Shuffle the blocks, turn some pieces to other edges, and add a block cut in a new shape from a leftover square or a scrap of another color. Where does it tip into chaos? Photograph each arrangement if you can, and step back between them. Then choose the one that holds the most difference and still reads as one family.
8. Glue the arrangement you chose: a glue stick on the back of each block, then on each piece, painted side down. A glue stick is drier than liquid glue, so it is less likely to wrinkle the paper or wet the paint again. Press it under a book until the glue has set.

Take care: Cut with the blade moving away from your body, on a self-healing mat with your holding hand behind the metal ruler, and with an adult close by for younger learners. Use paints that carry the ACMI AP seal, cover the table, let the painted sheets dry fully before you cut, and rinse brushes before the paint dries in them.

Take it further

Study Kōrin’s restraint at scale. Set the sheet long and low, such as 20 by 5 inches, and repeat one small cluster of three or four cuts across it several times with Copies. Vary only the spacing and grouping between clusters, never the clusters themselves, and see how much difference spacing alone can carry.

Reflect

• Which single change added the most interest for the least disorder?
• At what step did your design tip into chaos, and what changed at that step?
• Could viewers sort your three designs correctly, and what did they use as evidence?
• How is the variety in your design different from emphasis, where one thing is made to stand out?

What to look for

• Every cut is recognizably related to the parent shape.
• The learner can name and justify each difference in the design.
• The design shows at least three kinds of difference without losing its family resemblance.
• The chaos design differs from the middle design in kinds of difference, not in number of cuts.
• The painted papers differ in one quality only, in steps the eye reads as even, and the grid keeps every block in its row and column.