Geometric and Organic Twins

The idea: shape

A shape is a flat, enclosed area with height and width but no depth. Shapes may be geometric, regular and measurable like circles and squares, or organic, irregular like leaves and clouds, and they may be positive, the subjects, or negative, the spaces around them.

In a notan: In a notan every cut makes the same shape twice. Inside the sheet it is a negative shape, a hole that shows the ground; beyond the edge it is a positive shape, a piece that shows the back of the paper. The two are exact mirror images, so a circle or a square lands looking just as it did, while a leaf or a bird lands as its mirror twin, facing the other way. The sheet is a shape too. It begins as a plain rectangle, and every cut makes it more particular, until the paper left standing is often the most interesting shape in the design.

Every shape belongs to two families at once. By character it is geometric, made of straight lines, true curves and measurable angles, or organic, irregular and alive, like a leaf or a puddle. By role it is positive, a figure, or negative, the space around one. A notan puts both pairs to work, because each cut is a negative shape inside the sheet and, after the fold, a positive shape outside it. The studio’s tools divide along the first pair: Rectangle, Ellipse, Triangle and Hexagon make geometric shapes in one drag, while Draw and the Pen make whatever your hand can describe.

The fold adds a test no drawing can. A mirror reverses the shape, so a piece looks exactly like its hole only if the shape has a line of symmetry parallel to the edge it folds over. A circle passes every time. The studio’s triangle, which stands point up, lands unchanged when it folds left or right, but folded up or down it lands point down. An organic shape almost never has such a line, so its piece is a mirror twin, the way a left hand is the twin of a right. Predicting this before you press an arrow is the start of designing with the fold instead of being surprised by it.

Art history

The twentieth century argued about shape. Some artists wanted the pure shapes of geometry, which seemed modern and universal; others wanted shapes that looked grown rather than built. Sometimes the argument happened inside one household: Sophie Taeuber-Arp and Jean Arp, who were married, often worked on different sides of it. Cut paper let artists decide a shape in a single move of the scissors, and two of the works below were made that way.

• Jean (Hans) Arp Enak’s Tears (Terrestrial Forms), 1917 Museum of Modern Art, New York

  The fluid, lobed shapes of this painted wood relief look poured, grown or worn smooth by water rather than measured. They are organic shapes with no obvious subject, which makes them ideal to study: you see the character of the shape itself, not a thing it represents.

• Sophie Taeuber-Arp Composition, 1930 Museum of Modern Art, New York

  The painting is also known as Composition of Circles and Overlapping Angles, a title that names the two geometric families in play. Yet the painting is not stiff. Its life comes from how the shapes are placed, how they touch and how they cross, a reminder that geometric shapes carry feeling through arrangement.

• Ellsworth Kelly Study for White Plaque: Bridge Arch and Reflection, 1951 Museum of Modern Art, New York

  In Paris, Kelly took this shape from the arch of a bridge over the Seine together with its reflection in the water, and recorded it in cut and pasted paper. It is the notan’s own trick found in the street: a shape and its mirror image, joined along a line, make a new shape neither half suggests alone.

• Henri Matisse The Parakeet and the Mermaid, 1952–53 Stedelijk Museum, Amsterdam

  In his last years Matisse cut shapes directly from sheets his assistants had painted with gouache, then had them pinned up and moved until they sat right. This wall of leaves, fruit, a bird and a mermaid is organic shape at full scale. Notice how the leaves resemble one another without matching, so the family reads as grown, not manufactured.

Design today

Designers choose between geometric and organic shape as a matter of voice. The octagon that Chermayeff & Geismar designed for the Chase Manhattan Bank in 1960 is pure geometry: four identical angular pieces turning around a small square of empty space. It says precision and stability, and the empty square in the middle is a negative shape doing half the work. Maija Isola’s Unikko print for Marimekko, from 1964, speaks in the other voice: huge poppies whose organic shapes feel grown rather than drafted.

Most working marks mix the families on purpose, and app icons are commonly drawn on a shared grid of circles and squares so that a set agrees even when the pictures differ. Look at any logo built from a single silhouette and ask the notan questions: is it geometric or organic, is the mark the positive shape or the space around it, and would it still work flipped?

Warm-up

Sort a pile of objects or pictures into two groups, geometric and organic, and argue about the borderline cases: is an egg geometric? Is a crescent moon? Then fold a scrap of paper in half and cut a half-shape from the fold, once geometric and once organic, and open them. The fold has made each shape symmetrical, as Kelly’s arch and its reflection are. In a notan, a cut that touches the edge of the sheet does the same thing in two values.

In the studio

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

1. Open the studio. In the ‘Colors’ cards on the Color tab, select ‘Back’ and give it a color clearly different from the black front, with its sliders or a hex code, so holes, pieces and sheet are easy to tell apart.
2. Make three geometric cuts: a square with Rectangle and a circle with Ellipse, pressing Shift once each drag has begun, and a Triangle. Before each flip, write down how you think the piece will land, then press an arrow. Fold the triangle up or down and check it lands point down.
3. Make three organic cuts with Draw, each in one stroke: a leaf, a bird and a shape of your own invention. Fold each over a different edge; every one lands as its mirror twin. If you prefer another direction, press Undo at once: the chooser reopens with the same shape waiting.
4. Refine one organic shape. With Points, drag anchors and handles until the silhouette is unmistakable; with Curves, click an anchor to make a sharp corner, such as a beak or a leaf tip, or drag from it to round it. The piece changes with the hole as you work.
5. Find where the families meet. Select a circle with Points, click its outline to add an anchor and pull it out into a lobe: is it still geometric? Then click every anchor of an organic shape with Curves until its sides straighten into a polygon. Where did each change families?
6. Compose. Keep or delete cuts until the sheet holds a clear conversation between the families, perhaps a row of geometric holes along one edge broken by a single organic shape. Select the geometric shapes with Move and use Align, its switch on ‘Sheet’, to set them true to the paper, and leave the organic ones where your hand put them.

With paper and paint: Brush Shapes, Blade Shapes

Every tool has a family of shapes it makes easily. A loaded brush makes organic shapes almost by itself: press and a leaf swells, lift and it tapers, let the paint pool and an edge wanders. A ruler and blade make straight sides and true corners just as easily, and fight every curve. Feeling which tool resists which shape is the quickest way to understand the two families. Painting before cutting is also how Matisse worked in his last years, cutting shapes from sheets painted with gouache, so that the color came first and the scissors found the shape. Paper adds one lesson the screen cannot: there is no Undo, so every prediction about the flip is a real bet.

1. Paint the back. Tape the square to the covered table by its corners and brush one side with an even coat of a strong color, such as orange. This side is the back: only the flipped pieces will show it, so every piece will stand apart from the white sheet and the black ground. Let it dry right through.
2. Paint organic shapes. Turn the square white side up and tape it again. With the round brush and black paint, paint three organic shapes without drawing first: press the belly of the brush down and lift it to make a leaf, twist it as you press to make a petal, and let a third shape grow as you push a small wet patch outward with the tip, keeping it thin enough to dry flat. Then, on the scrap, try to paint a perfect circle. Which was easier? Let the paint dry.
3. Draw geometric shapes in the spaces left. With the pencil and ruler, draw a square and a triangle standing point up, and trace around a coin or bottle cap for a circle. Keep every shape clear of the others. Choose the edge each piece will flip over, and write down how you think it will land.
4. Cut the geometric shapes. Each lies inside the square, so start each one on its outline with a short slit made by the knife, an adult making it for younger learners, and cut the rest with scissors; a snip started inside the shape would split its piece, and the piece is half the design. Older learners can cut the straight sides with the knife against the metal ruler. Notice how the ruler makes a straight side easy and a curve impossible.
5. Cut the organic shapes with scissors, starting each from a short slit on its outline in the same way, following the painted edge and turning the paper, not the scissors, into each curve. Where the paint wobbles or bleeds, decide whether to follow it or smooth it. The brush found the shape; the scissors must commit to it.
6. Glue the square, white side up, in the middle of the black ground. Turn each piece over the edge you chose, colored side up, and place it as far outside the edge as its hole sits inside. Check your predictions: the square and the circle land looking like their holes, the triangle turned over the top edge lands point down, and every painted shape lands as its mirror twin.
7. Look at the holes where the painted shapes were. The black ground fills each one in the shape the paint made, now with a cut edge. Glue each piece once you are sure of its place, then set the sheet beside your screen design. Which family did each tool favor, and which shape changed character when its brush edge became a cut edge?

Take care: Let each side dry right through before you paint the other or cut, since damp paper tears; choose paints with the ACMI AP seal, and rinse brushes before the paint dries in them. Cut on a self-healing mat, away from your body, with the hand that holds the ruler well clear of the blade’s path, and let an adult make the starting slit inside a shape for younger learners.

Take it further

Photograph three shapes near home or school, one geometric, one organic and one on the border, and bring one in with Trace a photo, traced as a single shape. Is its silhouette more recognizable than the one you drew by hand, or less? Then use Copies with a move and a turn to set a ring of geometric shapes around your organic one, like a rosette in a folk paper cut.

Reflect

• Which of your shapes was hardest to classify as geometric or organic, and what finally decided it?
• Which of your predictions about the flip were wrong, and what did the mistake teach you about symmetry?
• Where in your design does a geometric shape make an organic one look more alive, or the other way around?
• How is Kelly’s bridge arch and its reflection like a cut that touches the edge of your sheet?

What to look for

• The design includes both geometric and organic shapes, and the learner can say which is which.
• Predictions about how each piece would land were recorded before flipping.
• At least one organic silhouette is recognizable from its outline alone.
• The contrast between the two families of shape is deliberate, not accidental.
• On the painted sheet, organic shapes were painted freely and cut along their painted edges, and geometric shapes were measured and cut straight.