The hammer rang once. A spark jumped off the anvil and did not go out. It waited. They followed.

Lan was already running. Lan was always already running. Inkling came behind her, walking fast, with her hands in her coat pockets.

It was the kind of grey morning when the Green smells of wet grass and somebody's toast. The spark bobbed along in front of them, past the mending shed, past the bench where somebody always fed the sparrows, and right up to the door of the print shop. Then it hung there in the air, glowing, the way a dog sits by the door when it wants to go out.

"Again!" said Lan. "It wants us again!"

"It came back for us," said Inkling. "I noticed it waited longer this time."

Inside, the print shop was warm. There were drawers full of metal letters, and stacks of paper in every colour, and the long table down the middle where everybody worked. The spark floated over the table and settled beside a square of paper, orange on one side and cream on the other.

The square sat up, the way it always did, as if it had just woken up and was pleased to see them.

"Fold me, I won't mind," said Kami.

"Can we go somewhere new?" asked Lan. "Not Kuwana. I mean, I liked Kuwana. But somewhere new."

"Every fold makes me something new," said Kami. "Start with something you know. Start with a little book."

They knew the little book. It was the very first thing anybody learned at the print shop. Inkling laid Kami flat, cream side up. Lan brought the top edge down to meet the bottom edge, and Inkling ran her finger along the fold to make it sharp. Then they opened it a little, so it stood up like a book with its covers apart.

The last crease went flat, and the paper opened like a door.

The book opened wider than any book could open. It opened until the space between its covers was a gravel path, with a hedge on one side and a high brick wall on the other.

Lan stepped through. Inkling stepped through behind her, holding Kami by one corner.

They were standing in a garden. It was not a grand garden, with fountains. It was a working garden. There were rows and rows of small flower beds, each one no bigger than a doormat, edged with little stones. There was an apple tree with a few last red apples high up. There was a wooden shed with a watering can hanging on a nail.

But every flower bed was empty. There were only brown stalks and a few curled leaves. It was autumn, and the leaves on the apple tree were turning yellow and letting go, one at a time.

"Where are we?" whispered Lan.

Inkling looked at everything. A woman went by in a long grey dress with an apron over it, carrying a basket of firewood. A boy ran past in short trousers and boots that buttoned up the side.

"Somewhere cold," said Inkling. "And a long time ago. Their clothes are old."

Kami crackled softly. "A garden in Bad Blankenburg, in Germany," said Kami. "It is the 1840s. The people here have a new word for this place. They call it a kindergarten."

"Kinder means children," said Inkling. "I think. And garten is garden."

"A children's garden," said Kami. "The children are the ones growing."

Under the apple tree there was a long wooden table, and around it sat children much smaller than Lan. Some of them were only four or five. Every child had a little pile of coloured paper squares in front of them, red and green and blue and yellow, and every child was folding.

One of the table's legs had cracked once and been mended with a strip of tin, nailed neatly round. Beside the tin, so small you would only see it if you were four years old and sitting very close, a tiny hammer had been scratched into the wood.

One girl had folded a square into a small boat and was sailing it across the table. Another had folded four corners into the middle, again and again, and made a pattern like a star with a star inside it. A boy had folded a square in half, and in half again, and was counting the little squares he had made with his finger, out loud, very seriously.

At the end of the table sat an old man with grey hair that stood up a little at the back. He wore a plain dark coat. He was folding a paper star of his own, with long, careful fingers. Every now and then a child held up their paper to show him. He looked at it properly, every time, and nodded. But he did not explain anything.

"He's like the monk," whispered Lan. "He just folds."

"He lets them work it out," said Inkling. "I noticed that."

Not every child was at the table. A boy sat on his own at the edge of the path, beside one of the little flower beds. He was about six. He had a brown jacket that was too big for him, so the sleeves were turned back twice, and he was holding a single blue square on his knee. He was not folding it. He was just looking at the empty bed.

Lan, who was never shy for long, went straight over.

"Hello," she said. "I'm Lan. This is Inkling. That's Kami."

The boy looked at the talking paper with very round eyes. Then he decided not to mind, the way people in these stories always seemed to.

"I'm Emil," he said. "This is my bed. Everybody gets one. You plant things in it and look after them."

"But it's empty," said Lan.

"It's autumn," said Emil. "My flowers were marigolds. They were orange, like that." He pointed at Kami. "They're all gone now. It's not their fault. It's just autumn."

He looked down at the blue square.

"My little sister Liese starts here tomorrow," he said. "She's only four. She doesn't want to come. She says it's too big and she doesn't know anybody. She cried last night."

"Poor Liese," said Inkling.

"I wanted to give her a flower," said Emil. "From my bed. So she'd know somebody here was glad she came. But there aren't any flowers. And if I picked one from somewhere else, it would wilt by tomorrow anyway."

He held up the blue square. "So I thought, a paper one. A paper flower doesn't wilt. But I only have one square, and I don't know how."

Lan looked at the blue square. She looked at the empty bed. Then she had an idea, and her ideas always came out of her mouth before they had finished arriving.

"I'll make her one!" said Lan. "I promise. A flower is easy. You just need a wavy edge, like petals. Watch."

She took the blue square and began to tear it with her fingers, round and round the edge, to make it wavy.

"Not all the way through, please!" said Kami.

Lan froze, with her fingers pinching the paper.

"A torn shape is just a flat scrap," said Kami. Its voice was crackly and small, but very clear. "It would lie on the ground like a leaf. It could never stand up in the bed. Every fold makes me something new. Nothing has to be torn away. Leave me whole, and fold me."

Lan looked at the square. There was a small tear at one edge, no longer than her fingernail. She thought about a flat blue scrap lying on the empty bed, and Liese looking at it, and not knowing it was meant to be a flower.

Her ears went hot. She gave the square back to Emil very carefully.

"I said easy before I checked," she said quietly. "Sorry, Emil."

Emil looked at the little tear. He smoothed it with his thumb.

"It's only a small one," he said. "It's still one square. That's what counts."

Inkling noticed that Lan's ears stayed hot for a long time afterwards. She noticed that Lan did not say "easy" again all morning.

"Can we watch them first?" asked Inkling. "The children at the table. I want to see what they make."

So they stood behind the long table and watched, the way you watch somebody doing a thing they are good at.

The girl with the boat had made a whole fleet now, red and green and blue, and was lining them up in a row. A boy beside her was making a little house with a pointed roof. Another was making a cup, the same cup Lan and Inkling had folded to get to Kuwana.

"Those are things," said Inkling. "Boats. A house. A cup. Things you'd know if you saw them."

Further along, three girls were folding patterns. They folded the four corners of a square into the middle. Then they turned it over and folded the corners into the middle again. Then they opened some flaps and turned them back, and the square grew a pattern like a window in a church, or a snowflake. Every pattern was the same on the left as on the right, and the same at the top as at the bottom.

"Those aren't things," said Lan. "They're just pretty."

"They match," said Inkling. "Both sides match. Like a butterfly."

At the far end, the serious boy had finished counting. He had folded his square in half, and in half again, and in half one more time. When he opened it out, the creases had divided it into eight little rectangles, all exactly the same size. He showed the old teacher, and pointed, and counted them again: one, two, three, all the way to eight.

"That one isn't a thing, and it isn't pretty," said Lan. "It's sums."

"It's knowing," said Inkling. "Halves and quarters. Knowing how much."

Kami leaned in Inkling's hand. "The people here say there are three kinds of folding," said Kami. "Folds of life, which are things you know. Folds of beauty, which match. And folds of knowledge, which teach you how much."

Lan thought about it. "So which kind is a flower?"

"That," said Kami, "is a very good question."

Emil sat at the end of the long table with his blue square. Lan sat on one side of him and Inkling on the other. The old teacher was still folding his star. He looked up when they sat down, and looked at Emil's square, and looked away again, kindly, as if he was leaving room.

Someone very particular came hurrying along the bench.

"Corners first, always," said Cornelia.

Cornelia was very particular about corners. She bustled up beside Emil and pointed at the square. "Turn it so a corner points at you. That's it. A diamond. Now the bottom corner goes up to meet the top corner. Make the corners meet exactly."

Emil brought the bottom corner up. It reached the top corner, but only nearly.

"Not quite," said Cornelia. "Exactly. Look at both points."

Emil moved it a tiny bit. Now the two points sat one on top of the other, perfectly.

"Point to point, then hold," said Cornelia. "Hold it still with one finger. Now press the fold."

He pressed. The square was a triangle, pointing up at the apple tree. It was two layers thick. Each layer was exactly half of the square.

"It's a tulip!" said Inkling.

Everybody looked at her.

"It's a triangle," said Lan. "Tulips have petals. That's a mountain. Or a tent."

Inkling went pink, and then laughed. She had named it too soon. That was her habit, and she knew it was her habit, and it still got out before she could stop it.

"It is a half, though," she said. "I can name that properly. It's half of a square. Two layers, and each one is a half."

"So it's a fold of knowledge," said Lan slowly. "Already."

"Bring it all the way over, next time, without me telling you," said Cornelia to Emil, very pleased. "You did it."

"What now?" asked Emil. He held the blue triangle carefully, with both hands, as if it might fly off.

On the table, in front of the old teacher, lay a stack of cards. Each card had a drawing on it. Inkling leaned over and saw a boat on one, and a star on another. Near the bottom of the pile was a card that showed a triangle with two dashed lines on it, one on each side.

Someone was already looking at it. It was Mark, who drew every fold line in the world and liked nothing better than a good drawing. Mark had a pencil behind one ear and a ruler in his hand.

"Read the drawing before your hands move," said Mark. "Every line on the drawing has a job."

They all crowded round. Kami leaned in too.

"Dashes mean fold," said Mark, and he traced the first dashed line with his finger. "This line starts at the bottom, near the middle. It goes up and out to the side. So this corner, the left one, folds up along it. Up and past the top point."

"Past the top?" asked Emil.

"Past the top," said Mark. "Look where the line stops. It stops right there, by the middle. So the corner swings all the way up and pokes out over the top. That's one petal."

He moved his finger to the other side of the drawing.

"And here," said Mark, "is the same line again. On the other side. Do you see? It's exactly like the first one, only turned round. Like a picture in a mirror."

Inkling looked from one line to the other. "One line, and the same line again," she said. "That's two lines."

"One plus one is two," said Mark. "Two lines. Two petals. And because the second is a mirror of the first, the two petals will match."

"Match," said Lan. "Like the patterns those girls were making. Both sides the same."

"A fold of beauty," said Inkling, and then put her hand over her mouth. "Wait. I can name it. No, I really can this time. It's a fold of beauty because it matches."

"Read it twice before you fold it once," said Mark, and he tapped the card and put it back on the pile.

Emil took a breath. He lifted the left corner of the triangle and brought it up along Mark's line, up and past the top point. He pressed it gently. It stood up like a little blue flame.

"One petal," whispered Lan.

Emil lifted the right corner. He was going faster now, because the first one had been so easy. He swung it up past the top.

It went crooked.

It did not go up along the line. It leaned out sideways, away from the first petal, so the flower looked like it was trying to wave goodbye. The two petals did not match at all. One stood straight and one leaned.

Emil stared at it. His mouth went wobbly at the corners.

"I've spoiled it," he said. "It doesn't match. Liese will think it's a broken one."

Then someone very cheerful came bouncing along the bench. It was Crinkle, who loved mistakes almost as much as other people love cake.

"Crooked is just a first go," said Crinkle. "We can fix this one. Open it up gently."

Emil sniffed. He opened the crooked petal, slowly, so it lay down flat again.

"Smooth it out and try again," said Crinkle. "Look. The crease remembers."

They all looked. On the paper there were two creases now. One was the crooked one, leaning out. The other was a faint line that Emil had nearly made before he hurried, running exactly where Mark's dashes had been.

"The crease remembers where you went," said Crinkle. "So it can show you where you meant to go. Use the first petal like a mirror."

This time Emil did not hurry. He looked at the first petal standing straight. Then he lifted the second corner and brought it up along the faint line, slowly, slowly, watching the first petal the whole time, so the second would be its twin.

It went up straight. It stood beside the first petal, leaning in, exactly the same.

Crinkle did a little bounce of joy. "See? First go, second go. That's all mistakes are."

"It matches," said Emil. He laughed, a short surprised laugh. "It actually matches."

The tulip was nearly done, but the petals were soft. When Emil let go of them, they started to open out again, slowly, as if the paper was tired and wanted to lie down.

Someone slow and calm came walking along the path. It was Presso, who never hurried and never needed to.

"Hold it still," said Presso. Presso's voice was low and patient, like a cello. "Now press it flat. Run your thumbnail along the fold."

Emil held the first petal still and ran his thumbnail along its fold, from the bottom to the top.

"Press slowly, press firmly," said Presso. "A fold you press is a fold that stays."

Emil pressed the first petal. Then he pressed the second. He pressed the bottom fold, the very first one, the corner to corner one, one more time for luck. This time when he let go, the petals did not open. They stayed. The tulip stayed a tulip.

He carried it over to his empty flower bed and stood it in the middle, propped against a stone. It stood up, blue against the brown earth, with its two petals pointing at the sky.

They all stood and looked at it.

"It's a flower," said Lan. "A real one. I mean, a paper one. But it stands up."

Inkling was quiet for a long time. When she spoke, she spoke slowly, as if she was naming something very carefully this time.

"It's three things," she said. "It's a fold of life, because it's a flower, and everybody knows a flower. The petals match on both sides, so it's a fold of beauty. And the very first fold made a half, two layers, each half of the square. So it's a fold of knowledge too."

"All three kinds," said Lan. "In one square."

"In one square that nobody tore," said Kami.

At the end of the long table, the old teacher had finished his star. He looked over at the little blue tulip in the empty bed. He looked at it properly, the way he looked at every child's paper. Then he nodded, just once, and went back to his folding.

They stayed until the next morning, because they wanted to see.

They waited by the garden gate with Emil. The sky was clear and cold, and their breath made little clouds. The apple tree had dropped three more leaves in the night.

A woman came up the lane holding a small girl by the hand. The girl had a red knitted hat and two thin plaits, and she was holding her mother's hand so tightly that her knuckles had gone white. She was looking at the high brick wall as if it might swallow her.

"That's Liese," whispered Emil.

He went out through the gate. He did not say anything at first. He just held out the blue tulip.

Liese looked at it. She looked at Emil.

"It's for you," said Emil. "From my bed. It won't wilt. Not all winter. Not even if it snows."

Liese took it. She turned it round in her fingers. She touched one petal, and then the other, and Inkling saw her notice that they matched.

"You made it?" asked Liese.

"With some help," said Emil. "It's a tulip. There are three kinds of folding, and it's all of them."

Liese did not know what that meant. But she held the tulip up to the light, and the sun came through the blue paper and made the petals glow.

Then she let go of her mother's hand. Not all at once. Just one finger at a time. And she walked through the gate into the children's garden, holding the tulip in front of her like a lantern.

"She came in," said Lan.

"Because somebody here was glad she came," said Inkling.

The garden was busy now. Children were arriving, and the long table was filling up, and somebody was already showing the old teacher a new boat.

"How do we get home?" asked Lan.

Kami crackled. "Fold me all the way, and the paper opens," said Kami. "Unfold me flat, and you are home."

Lan found a plain square in her pocket that she did not remember putting there. It had a little book shape creased into it. She and Inkling unfolded it together, edge by edge, until it lay perfectly flat.

They unfolded the paper flat, and the door closed behind them.

They were standing at the long table in the print shop. The paper stacks were exactly where they had been. Kami lay on the table, a plain square again.

The spark dimmed to a warm dot and settled back on the anvil. The Green was just the Green again.

Back on the Green

That afternoon, the print shop was making valentines, even though it was nowhere near Valentine's Day. Lan wanted to make a paper heart. She picked up a red square and started to tear round the edge, fast.

She stopped. She looked at the square. Then she folded it in half first, edge to edge, and tore only along one side. When she opened it out, both sides of the heart were exactly the same.

"A fold of beauty," she said, pleased.

Inkling was sitting at the end of the table with a yellow square. She folded it corner to corner and held up a triangle.

"Is it a tulip?" asked Lan.

"Not yet," said Inkling. "But it is a half. I can name that."

Tell the story back to someone. What three kinds of folding were in one tulip, and why did nobody tear the square?