# world.lapla.si — Laplace’s Mini World (拉普拉斯的迷你世界)

> Interactive 3D science models in the browser, each with a short illustrated essay and a laboratory to try things in. Chinese (zh) and English (en). No accounts, no ads. Licence: CC BY-NC 4.0.

Every model can be shown on its own, sized to its frame: https://world.lapla.si/embed/{lang}/{slug}/ (?chapter=<id>, ?lab=1, ?theme=light|dark, lab settings by id). The full catalog, with chapters and lab settings, is https://world.lapla.si/models.json. AI chats can connect to the MCP server at https://world.lapla.si/mcp (tools: search_models, show_model, list_chapters); oEmbed: https://world.lapla.si/oembed?url=<plate URL>.

When citing a plate, link its page (https://world.lapla.si/en/{slug}/ or https://world.lapla.si/zh/{slug}/, not the embed page) and name the site, e.g. Laplace’s Mini World, Plate 10, “How the Moon Moves the Sea”, https://world.lapla.si/en/tides/, CC BY-NC 4.0. Every plate page ends with its own citation line and carries schema.org LearningResource data.

## Catalog

- [API and MCP docs](https://world.lapla.si/en/api/) ([中文](https://world.lapla.si/zh/api/)): connecting the MCP server in ChatGPT, Claude and other clients; the fields of models.json; embed parameters; oEmbed; licence and how to cite
- [models.json](https://world.lapla.si/models.json): every plate with titles, summaries, chapters, embed URLs and lab settings
- [MCP server](https://world.lapla.si/mcp): Streamable HTTP, read-only
- Every plate's words as Markdown: https://world.lapla.si/{lang}/{slug}/index.html.md (the essay, notes, sources, licence and how to cite)
- [llms-full.txt](https://world.lapla.si/llms-full.txt): every plate with its chapters and lab settings

## Nature / Space

- [Halley’s Comet Is Far Away. Its Dust Is Here. (哈雷彗星还在远方，它的尘埃先到了)](https://world.lapla.si/en/orionids/): plate 40. Every late October the Earth ploughs through dust shed by Halley’s Comet, and the Orionids streak across the night. In 2026 the best night is October 21 to 22. Markdown: [en](https://world.lapla.si/en/orionids/index.html.md), [中文](https://world.lapla.si/zh/orionids/index.html.md).
- [The Shadow of the Moon (月亮的影子)](https://world.lapla.si/en/eclipse/): plate 03. The Sun is about 400 times wider than the Moon, and about 400 times farther away. That coincidence lets day turn to night for a few minutes. Markdown: [en](https://world.lapla.si/en/eclipse/index.html.md), [中文](https://world.lapla.si/zh/eclipse/index.html.md).
- [Why Summer Is Warm (夏天为什么热)](https://world.lapla.si/en/seasons/): plate 05. Not because the Earth is closer to the Sun. In early January the Earth is at its closest — in the dead of the northern winter. Markdown: [en](https://world.lapla.si/en/seasons/index.html.md), [中文](https://world.lapla.si/zh/seasons/index.html.md).
- [How the Moon Moves the Sea (月亮怎样拉动大海)](https://world.lapla.si/en/tides/): plate 10. Why are there two high tides a day? Because the Moon pulls the near ocean toward it — and leaves the far ocean behind. Markdown: [en](https://world.lapla.si/en/tides/index.html.md), [中文](https://world.lapla.si/zh/tides/index.html.md).
- [Why the Moon Changes Shape (月亮为什么会变脸)](https://world.lapla.si/en/moon/): plate 12. The Moon never changes shape. What changes is how much of its sunlit half we can see. Markdown: [en](https://world.lapla.si/en/moon/index.html.md), [中文](https://world.lapla.si/zh/moon/index.html.md).
- [The Space Station Is Falling (一直在下落的空间站)](https://world.lapla.si/en/orbit/): plate 18. Astronauts float not because there is no gravity in space, but because they and their station are always falling. Markdown: [en](https://world.lapla.si/en/orbit/index.html.md), [中文](https://world.lapla.si/zh/orbit/index.html.md).
- [Why a Foucault Pendulum Turns (傅科摆为什么会转)](https://world.lapla.si/en/pendulum/): plate 22. A long pendulum swings back and forth, and the line of its swing slowly turns. What turns is the floor beneath it, and the Earth beneath the floor. Markdown: [en](https://world.lapla.si/en/pendulum/index.html.md), [中文](https://world.lapla.si/zh/pendulum/index.html.md).
- [The Solar System Today (今天的太阳系)](https://world.lapla.si/en/planets/): plate 24. Where are the eight planets right now? The farther from the Sun, the slower they go, and the longer a lap takes. Markdown: [en](https://world.lapla.si/en/planets/index.html.md), [中文](https://world.lapla.si/zh/planets/index.html.md).
- [What Pushes a Rocket (火箭靠什么飞上天)](https://world.lapla.si/en/rocket/): plate 27. A rocket doesn’t push against the air. It throws a large part of itself backwards very fast, and the rest of it is pushed forwards. Markdown: [en](https://world.lapla.si/en/rocket/index.html.md), [中文](https://world.lapla.si/zh/rocket/index.html.md).
- [Where Not Even Light Escapes (连光都逃不出来的地方)](https://world.lapla.si/en/blackhole/): plate 38. A black hole packs so much matter into so small a space that not even light can get out. It is dark itself, but the light it bends around it draws a bright ring. Markdown: [en](https://world.lapla.si/en/blackhole/index.html.md), [中文](https://world.lapla.si/zh/blackhole/index.html.md).

## Nature / Earth & Sky

- [How Rain Carves a Mountain (雨水如何雕刻一座山)](https://world.lapla.si/en/erosion/): plate 01. A single storm changes almost nothing. But the rain never stops. Markdown: [en](https://world.lapla.si/en/erosion/index.html.md), [中文](https://world.lapla.si/zh/erosion/index.html.md).
- [The Wave That Hides in Deep Water (藏在深海里的浪)](https://world.lapla.si/en/tsunami/): plate 02. Out at sea it is almost impossible to notice. At the coast it can drown a town. Markdown: [en](https://world.lapla.si/en/tsunami/index.html.md), [中文](https://world.lapla.si/zh/tsunami/index.html.md).
- [The Engine of a Hurricane (飓风的引擎)](https://world.lapla.si/en/hurricane/): plate 04. It runs on warm water, and the turning Earth sets it spinning. Markdown: [en](https://world.lapla.si/en/hurricane/index.html.md), [中文](https://world.lapla.si/zh/hurricane/index.html.md).
- [Curtains in the Sky (天上的帘幕)](https://world.lapla.si/en/aurora/): plate 11. An aurora is light given off when electrons from space crash into the air high overhead. Markdown: [en](https://world.lapla.si/en/aurora/index.html.md), [中文](https://world.lapla.si/zh/aurora/index.html.md).
- [The Cracks in the Earth (地球的裂缝)](https://world.lapla.si/en/quakes/): plate 14. A year’s 7,700 strong earthquakes fall mostly along a few lines: the edges of the pieces of the Earth’s shell. Markdown: [en](https://world.lapla.si/en/quakes/index.html.md), [中文](https://world.lapla.si/zh/quakes/index.html.md).
- [Where Volcanoes Come From (火山从哪里来)](https://world.lapla.si/en/volcano/): plate 19. There is no sea of magma under the crust. Magma forms in only a few kinds of places, and that is where volcanoes grow. Markdown: [en](https://world.lapla.si/en/volcano/index.html.md), [中文](https://world.lapla.si/zh/volcano/index.html.md).
- [Where a Compass Points (指南针指向哪里)](https://world.lapla.si/en/compass/): plate 23. A compass doesn’t point at the North Pole. It lines up with Earth’s magnetic field — and the magnetic pole it heads for keeps moving. Markdown: [en](https://world.lapla.si/en/compass/index.html.md), [中文](https://world.lapla.si/zh/compass/index.html.md).
- [Seeing Through the Earth With Earthquakes (用地震看穿地球)](https://world.lapla.si/en/core/): plate 25. No one has been to the centre of the Earth. We know it holds a liquid outer core and a solid inner core because earthquake waves went for us. Markdown: [en](https://world.lapla.si/en/core/index.html.md), [中文](https://world.lapla.si/zh/core/index.html.md).
- [Why Clouds Don’t Fall (云为什么不会掉下来)](https://world.lapla.si/en/cloud/): plate 30. An ordinary cumulus cloud holds hundreds of tonnes of water, yet it floats. The secret is how astonishingly small its droplets are. Markdown: [en](https://world.lapla.si/en/cloud/index.html.md), [中文](https://world.lapla.si/zh/cloud/index.html.md).
- [See the Flash, Then Hear the Thunder (先看见闪电，再听见雷)](https://world.lapla.si/en/thunder/): plate 33. Lightning and thunder happen at the same moment, but light arrives almost at once while sound covers only about 340 metres a second. Count the seconds between them and you know how far away the storm is. Markdown: [en](https://world.lapla.si/en/thunder/index.html.md), [中文](https://world.lapla.si/zh/thunder/index.html.md).
- [The V Behind a Ship (船尾的 V 字)](https://world.lapla.si/en/wake/): plate 35. A big ship, a small boat, even a swimming duck: the V-shaped wake behind them opens at almost exactly the same angle, about 19.5° on each side. Markdown: [en](https://world.lapla.si/en/wake/index.html.md), [中文](https://world.lapla.si/zh/wake/index.html.md).
- [Ice Rings Around the Sun (太阳周围的冰晶光环)](https://world.lapla.si/en/halos/): plate 49. In thin high cloud, the ice crystals are tiny hexagonal prisms. Sunlight passing through them paints rings, spots and coloured arcs around the Sun. Markdown: [en](https://world.lapla.si/en/halos/index.html.md), [中文](https://world.lapla.si/zh/halos/index.html.md).
- [Why Rivers Wind (河流为什么弯来弯去)](https://world.lapla.si/en/meander/): plate 50. Rivers on plains are rarely straight. In each bend the water swirls, cutting the outer bank and building the inner one, until the loop is cut off and left as an oxbow lake. Markdown: [en](https://world.lapla.si/en/meander/index.html.md), [中文](https://world.lapla.si/zh/meander/index.html.md).

## Nature / Life & Medicine

- [The Arithmetic of a Sunflower (向日葵的算术)](https://world.lapla.si/en/sunflower/): plate 06. Count the spirals its seeds make, and you will arrive at a famous sequence of numbers. Markdown: [en](https://world.lapla.si/en/sunflower/index.html.md), [中文](https://world.lapla.si/zh/sunflower/index.html.md).
- [No Bird in Charge (没有领头的鸟)](https://world.lapla.si/en/murmuration/): plate 09. Thousands of starlings turn together at dusk like a shape-shifting cloud of smoke. No one is giving orders. Markdown: [en](https://world.lapla.si/en/murmuration/index.html.md), [中文](https://world.lapla.si/zh/murmuration/index.html.md).
- [Where Spots and Stripes Come From (斑点和条纹从哪里来)](https://world.lapla.si/en/patterns/): plate 16. A leopard’s spots and a fish’s stripes may come from the same simple recipe: two ingredients, one fast and one slow. Markdown: [en](https://world.lapla.si/en/patterns/index.html.md), [中文](https://world.lapla.si/zh/patterns/index.html.md).
- [The Breathing Planet (会呼吸的地球)](https://world.lapla.si/en/breath/): plate 20. A tree’s wood is made mostly from air. Every summer the northern forests breathe in together, and the whole atmosphere holds less carbon dioxide. Markdown: [en](https://world.lapla.si/en/breath/index.html.md), [中文](https://world.lapla.si/zh/breath/index.html.md).
- [MRI Scanner (磁共振成像仪)](https://world.lapla.si/en/mri/): plate F03. A clinical MRI scanner: a superconducting magnet, gradient coils and RF coils, one inside another. Hydrogen nuclei precess in the field; their signal fills k-space, and a Fourier transform turns it into an image. Markdown: [en](https://world.lapla.si/en/mri/index.html.md), [中文](https://world.lapla.si/zh/mri/index.html.md).
- [Surgical Robot (手术机器人)](https://world.lapla.si/en/surgical-robot/): plate F04. The surgeon operates from a console nearby; the arms pivot each instrument about its incision. Hand motion is scaled down and stripped of tremor on its way to a tip 8 mm across. Markdown: [en](https://world.lapla.si/en/surgical-robot/index.html.md), [中文](https://world.lapla.si/zh/surgical-robot/index.html.md).
- [A Pattern Painted One Line at a Time (壳口一行行画出的花纹)](https://world.lapla.si/en/seashell/): plate 48. The triangles on a cone shell are painted at the edge of its opening, one line at a time. Each line is set by the cells along that edge: where one grows strong, it holds its neighbours back. Markdown: [en](https://world.lapla.si/en/seashell/index.html.md), [中文](https://world.lapla.si/zh/seashell/index.html.md).
- [Hearing a Moth in the Dark (在黑暗里听见飞蛾)](https://world.lapla.si/en/echo/): plate 52. A bat hunts at night by its own voice. It sends out calls too high for us to hear and listens for the echo off a moth; how late the echo comes back tells it how far away the moth is. Markdown: [en](https://world.lapla.si/en/echo/index.html.md), [中文](https://world.lapla.si/zh/echo/index.html.md).
- [How the Cochlea Takes Sound Apart (耳蜗怎样把声音拆开)](https://world.lapla.si/en/cochlea/): plate 53. Sound entering the ear ends up in a coiled tube. A membrane inside it is pushed into a wave that swells highest near the entrance for high notes and far along for low ones. A few thousand hair cells turn that motion into nerve signals. Markdown: [en](https://world.lapla.si/en/cochlea/index.html.md), [中文](https://world.lapla.si/zh/cochlea/index.html.md).
- [CRISPR-Cas9 Genome Editing (CRISPR-Cas9 基因编辑)](https://world.lapla.si/en/crispr/): plate F15. A ladder of DNA and a Cas9 built from its crystal coordinates: a guide RNA finds twenty letters among three billion, the PAM first, then base by base, and two domains cut one strand each. Markdown: [en](https://world.lapla.si/en/crispr/index.html.md), [中文](https://world.lapla.si/zh/crispr/index.html.md).

## Nature / Matter, Light & Sound

- [Why a Rainbow Is Round (彩虹为什么是圆的)](https://world.lapla.si/en/rainbow/): plate 07. It does not hang anywhere in the sky. It is a ring of light 42 degrees around the shadow of your own head. Markdown: [en](https://world.lapla.si/en/rainbow/index.html.md), [中文](https://world.lapla.si/zh/rainbow/index.html.md).
- [Why Snowflakes Have Six Points (雪花为什么有六个角)](https://world.lapla.si/en/snowflake/): plate 08. Every snowflake grows from one tiny six-sided crystal of ice. Markdown: [en](https://world.lapla.si/en/snowflake/index.html.md), [中文](https://world.lapla.si/zh/snowflake/index.html.md).
- [Why the Sky Is Blue (天空为什么是蓝的)](https://world.lapla.si/en/sky/): plate 13. The sky is not reflecting the sea. The air itself is throwing the blue in sunlight across the sky. Markdown: [en](https://world.lapla.si/en/sky/index.html.md), [中文](https://world.lapla.si/zh/sky/index.html.md).
- [How Sound Crosses the Air (声音怎样穿过空气)](https://world.lapla.si/en/sound/): plate 15. Sound is a push passed along through the air. The air doesn’t travel to you; the push does. Markdown: [en](https://world.lapla.si/en/sound/index.html.md), [中文](https://world.lapla.si/zh/sound/index.html.md).
- [Why Ice Floats (冰为什么浮在水上)](https://world.lapla.si/en/ice/): plate 17. Freeze most liquids and the solid sinks in its own liquid. Ice floats. The secret is in the little hexagons water molecules build. Markdown: [en](https://world.lapla.si/en/ice/index.html.md), [中文](https://world.lapla.si/zh/ice/index.html.md).
- [Three Cones, a Million Colors (三种视锥，百万种颜色)](https://world.lapla.si/en/color/): plate 21. Sunlight holds a smooth sweep of colors, but our eyes see it with just three kinds of cells. Every color you see is those three cells taking a vote. Markdown: [en](https://world.lapla.si/en/color/index.html.md), [中文](https://world.lapla.si/zh/color/index.html.md).
- [Why a Siren Changes Its Tune (救护车为什么会变调)](https://world.lapla.si/en/doppler/): plate 26. An ambulance sounds higher coming towards you and lower going away. The siren hasn’t changed; its sound waves have been squeezed or stretched. Markdown: [en](https://world.lapla.si/en/doppler/index.html.md), [中文](https://world.lapla.si/zh/doppler/index.html.md).
- [Where a Bubble’s Colours Come From (肥皂泡的颜色从哪里来)](https://world.lapla.si/en/bubble/): plate 28. Soapy water has no colour, yet bubbles shimmer with every hue. The colour isn’t in the soap — it is in how thick the film is. Markdown: [en](https://world.lapla.si/en/bubble/index.html.md), [中文](https://world.lapla.si/zh/bubble/index.html.md).
- [A Curved Piece of Glass (一块弯曲的玻璃)](https://world.lapla.si/en/lens/): plate 29. Light bends a little as it passes from air into glass. Shape the glass into a curve and light passing through every part of it can meet at one point — which is how magnifying glasses, cameras and your eyes work. Markdown: [en](https://world.lapla.si/en/lens/index.html.md), [中文](https://world.lapla.si/zh/lens/index.html.md).
- [Why Metal Feels Cold (为什么金属摸起来更凉)](https://world.lapla.si/en/touch/): plate 31. A metal spoon and a wooden spoon left in the same room are exactly the same temperature, yet the metal one feels much colder. What your hand feels is how fast heat leaves it. Markdown: [en](https://world.lapla.si/en/touch/index.html.md), [中文](https://world.lapla.si/zh/touch/index.html.md).
- [Why Mountain Water Isn’t Hot Enough (山顶上的水为什么不够烫)](https://world.lapla.si/en/boil/): plate 32. At the top of Everest, water boils at about 70°C — too cool to hard-boil an egg, however long you wait. The temperature water boils at depends on how much air is pressing down on it. Markdown: [en](https://world.lapla.si/en/boil/index.html.md), [中文](https://world.lapla.si/zh/boil/index.html.md).
- [Why a Steel Ship Floats (钢铁做的船为什么能浮起来)](https://world.lapla.si/en/float/): plate 34. Drop a lump of steel in water and it sinks at once, yet the same steel built into a ship floats with ten thousand tonnes of cargo aboard. The secret is how much water the ship pushes aside. Markdown: [en](https://world.lapla.si/en/float/index.html.md), [中文](https://world.lapla.si/zh/float/index.html.md).
- [Where Is the Electron? (电子在哪里)](https://world.lapla.si/en/atom/): plate 36. Textbooks often draw electrons as little balls circling the nucleus. In fact an electron has no orbit. It is more like a cloud: all we can say is where it is likely to be. Markdown: [en](https://world.lapla.si/en/atom/index.html.md), [中文](https://world.lapla.si/zh/atom/index.html.md).
- [When Two Ripples Meet (两圈水波相遇时)](https://world.lapla.si/en/ripple/): plate 37. Drop two stones in water and their rings of ripples pass straight through each other. In some places they cancel out, and the water there barely moves. Markdown: [en](https://world.lapla.si/en/ripple/index.html.md), [中文](https://world.lapla.si/zh/ripple/index.html.md).
- [The Invisible Lines Around a Magnet (磁铁周围看不见的线)](https://world.lapla.si/en/magnet/): plate 39. Lay a sheet of paper over a magnet, sprinkle iron filings on it and tap gently: the filings line up in curves running from one end of the magnet to the other. They are drawing the shape of its magnetic field. Markdown: [en](https://world.lapla.si/en/magnet/index.html.md), [中文](https://world.lapla.si/zh/magnet/index.html.md).
- [Sand That Draws a Sound (沙子画出的振动)](https://world.lapla.si/en/chladni/): plate 47. Sprinkle sand on a metal plate and make it ring. The sand jumps away from the moving parts and gathers on the lines that stay still, drawing the shape of the vibration. Markdown: [en](https://world.lapla.si/en/chladni/index.html.md), [中文](https://world.lapla.si/zh/chladni/index.html.md).
- [Patterns Shaken Out of Oil (摇出来的花纹)](https://world.lapla.si/en/faraday/): plate 51. Shake a dish of oil up and down hard enough and the still surface suddenly wrinkles into squares, hexagons or stripes. It rises and falls at half the rate of the shaking. Markdown: [en](https://world.lapla.si/en/faraday/index.html.md), [中文](https://world.lapla.si/zh/faraday/index.html.md).

## Technology / Chips & Information

- [How a Phone Knows Where It Is (手机怎么知道你在哪里)](https://world.lapla.si/en/gps/): plate 41. Thirty-odd satellites, 20,200 km up, keep announcing the time. A phone only listens, and from how late each announcement arrives it works out where it is, to within a few metres. Markdown: [en](https://world.lapla.si/en/gps/index.html.md), [中文](https://world.lapla.si/zh/gps/index.html.md).
- [Light in a Glass Thread (光在玻璃丝里走)](https://world.lapla.si/en/fibre/): plate 42. Shine a light into a stream of water and the light bends with the stream. Today the same trick traps the internet in glass threads as fine as a hair and sends it across the Pacific. Markdown: [en](https://world.lapla.si/en/fibre/index.html.md), [中文](https://world.lapla.si/zh/fibre/index.html.md).
- [A Code That Survives Sand (埋掉一块，照样能扫)](https://world.lapla.si/en/qr/): plate 45. Bury part of a QR code in sand and a phone still reads it. The secret is in its spare bytes, which say nothing at all but can work out what went wrong and how to put it right. Markdown: [en](https://world.lapla.si/en/qr/index.html.md), [中文](https://world.lapla.si/zh/qr/index.html.md).
- [EUV Lithography Machine (极紫外光刻机)](https://world.lapla.si/en/euv/): plate F01. Light 13.5 nm long prints a chip’s circuits on silicon, four times smaller than the mask. It comes from tin droplets turned to plasma, and travels only by mirrors. Markdown: [en](https://world.lapla.si/en/euv/index.html.md), [中文](https://world.lapla.si/zh/euv/index.html.md).
- [The Dilution Refrigerator (稀释制冷机)](https://world.lapla.si/en/dilution/): plate F05. A superconducting quantum computer hangs from a gold-plated “chandelier”. Each stage is colder than the one above; the last is about 10 mK, hundreds of times colder than space. Markdown: [en](https://world.lapla.si/en/dilution/index.html.md), [中文](https://world.lapla.si/zh/dilution/index.html.md).
- [Gate-All-Around Transistor (环栅晶体管)](https://world.lapla.si/en/gaa/): plate F14. In today’s most advanced chips each switch is a few sheets of silicon 5 nm thick, wrapped on all four sides by a metal gate. The tighter the wrap, the more firmly it switches off. Markdown: [en](https://world.lapla.si/en/gaa/index.html.md), [中文](https://world.lapla.si/zh/gaa/index.html.md).

## Technology / AI

- [More Features Than Neurons (比神经元更多的特征)](https://world.lapla.si/en/superposition/): plate 43. A single neuron in a neural network often stands for several unrelated things. A model with just two neurons can arrange five features into a pentagon and keep them all. Markdown: [en](https://world.lapla.si/en/superposition/index.html.md), [中文](https://world.lapla.si/zh/superposition/index.html.md).
- [Pictures Out of Noise (从噪声里长出来的图)](https://world.lapla.si/en/diffusion/): plate 44. Many AI image generators start from random static and remove it, one step at a time. A small network does the same in your browser, and a cloud of dots slowly condenses into a knot. Markdown: [en](https://world.lapla.si/en/diffusion/index.html.md), [中文](https://world.lapla.si/zh/diffusion/index.html.md).
- [Learning by Heart, Then Learning the Rule (先背答案，再学会规律)](https://world.lapla.si/en/grokking/): plate 46. A small neural network learns to add hours on a 24-hour clock. It gets its practice questions right almost at once, by memorising them, and only long afterwards answers questions it has never seen. Inside, it has built clocks. Markdown: [en](https://world.lapla.si/en/grokking/index.html.md), [中文](https://world.lapla.si/zh/grokking/index.html.md).
- [Attention in Transformers (Transformer 的注意力)](https://world.lapla.si/en/attention/): plate F13. A two-layer, eight-head Transformer reads a sentence in your browser, one character at a time, and guesses the next. Each thread is one act of attention; its brightness is the weight. Markdown: [en](https://world.lapla.si/en/attention/index.html.md), [中文](https://world.lapla.si/zh/attention/index.html.md).

## Ideas / Mathematics

- [Life from a Smooth Rule (规则里游出的生命)](https://world.lapla.si/en/lenia/): plate M01. Melt the squares, the ticks and the life-or-death of Conway’s Game of Life, and a small thing swims out of the numbers, with a body and a tail, healing when it is bitten. Its whole law is one ring and one bell-shaped curve. Markdown: [en](https://world.lapla.si/en/lenia/index.html.md), [中文](https://world.lapla.si/zh/lenia/index.html.md).
- [Counting Clacks, Finding π (碰撞数出 π)](https://world.lapla.si/en/blocks/): plate M02. Two blocks and a wall, and a count of the collisions. Each time the large block gets 100 times heavier, the count gains another digit of π. Markdown: [en](https://world.lapla.si/en/blocks/index.html.md), [中文](https://world.lapla.si/zh/blocks/index.html.md).
- [Any Closed Line, Drawn by Turning Circles (转动的圆，画出闭合的线)](https://world.lapla.si/en/fourier/): plate M03. A chain of arrows, head to tail, each turning at a whole-number speed: the last tip can draw any closed line. Markdown: [en](https://world.lapla.si/en/fourier/index.html.md), [中文](https://world.lapla.si/zh/fourier/index.html.md).
- [One in Eight Random Tetrahedra Hold the Centre (随机四面体包住球心：八分之一)](https://world.lapla.si/en/tetra/): plate M04. Four random points on a sphere make a tetrahedron that holds the centre one time in eight. Three points on a circle: one in four. Markdown: [en](https://world.lapla.si/en/tetra/index.html.md), [中文](https://world.lapla.si/zh/tetra/index.html.md).
- [Why a Slanted Cut Through a Cone Is an Ellipse (斜切圆锥，切口是椭圆)](https://world.lapla.si/en/dandelin/): plate M05. Slice a cone at a slant and the cut is the same curve two pins and a string draw. Two spheres prove it. Markdown: [en](https://world.lapla.si/en/dandelin/index.html.md), [中文](https://world.lapla.si/zh/dandelin/index.html.md).
- [Half a Turn Is e to the iπ (转半圈，是 e 的 iπ 次方)](https://world.lapla.si/en/euler/): plate M06. eⁱᵗ is a point walking round the unit circle at a steady pace, its velocity always i times its position. After time π it is at −1. Markdown: [en](https://world.lapla.si/en/euler/index.html.md), [中文](https://world.lapla.si/zh/euler/index.html.md).
- [Determined, Yet Unpredictable (确定，却无法预测)](https://world.lapla.si/en/lorenz/): plate M07. Three simple equations, nothing random in them. Two starts a millionth apart have nothing in common twenty time units later. Markdown: [en](https://world.lapla.si/en/lorenz/index.html.md), [中文](https://world.lapla.si/zh/lorenz/index.html.md).
- [Random Bounces Pile Up into a Bell Curve (随机碰撞，堆出钟形曲线)](https://world.lapla.si/en/galton/): plate M08. On a Galton board each steel ball goes left or right at random at every pin. After a thousand balls, the bins always show the same bell curve. Markdown: [en](https://world.lapla.si/en/galton/index.html.md), [中文](https://world.lapla.si/zh/galton/index.html.md).
- [A Matrix Moves the Whole Plane (矩阵，是搬动整个平面的方式)](https://world.lapla.si/en/linear/): plate M09. A 2 × 2 matrix moves the whole plane at once: grid lines stay straight, parallel and evenly spaced, and the origin stays put. Its columns are where the two basis arrows land; its determinant is the factor by which areas grow. Markdown: [en](https://world.lapla.si/en/linear/index.html.md), [中文](https://world.lapla.si/zh/linear/index.html.md).
- [A Fold That Opens in One Pull (一拉就开的折痕)](https://world.lapla.si/en/miura/): plate M10. A sheet folded into parallelograms opens all at once when one corner is pulled, and closes all at once when it is pushed back. One angle sets every crease. Markdown: [en](https://world.lapla.si/en/miura/index.html.md), [中文](https://world.lapla.si/zh/miura/index.html.md).
- [Slope and Area Undo Each Other (斜率与面积互为逆运算)](https://world.lapla.si/en/calculus/): plate M11. The derivative is the slope of a curve at a point; the integral is the area under it. The rate at which the area grows as the right edge moves is exactly the curve’s height there, so each operation undoes the other. Markdown: [en](https://world.lapla.si/en/calculus/index.html.md), [中文](https://world.lapla.si/zh/calculus/index.html.md).
- [Every Two Circles Linked (每两个圆都扣在一起)](https://world.lapla.si/en/hopf/): plate M12. The three-dimensional sphere in four-dimensional space falls apart into circles that never meet, one for each point of an ordinary sphere. Projected into three dimensions, every two of them are linked. Markdown: [en](https://world.lapla.si/en/hopf/index.html.md), [中文](https://world.lapla.si/zh/hopf/index.html.md).
- [Opposite Points, Same Weather (对面的点，同样的天气)](https://world.lapla.si/en/borsuk/): plate M13. At any moment there are two exactly opposite points on Earth with the same temperature and the same pressure. That is the Borsuk–Ulam theorem: a continuous map from the sphere to the plane always sends some pair of opposite points to the same place. Markdown: [en](https://world.lapla.si/en/borsuk/index.html.md), [中文](https://world.lapla.si/zh/borsuk/index.html.md).
- [One Shape, Never Repeating (只用一种形状，永不重复)](https://world.lapla.si/en/hat/): plate M14. A thirteen-sided shape made of eight kites covers the whole plane, yet however it is laid, the pattern never repeats periodically. Markdown: [en](https://world.lapla.si/en/hat/index.html.md), [中文](https://world.lapla.si/zh/hat/index.html.md).
- [A Sphere Will Not Lie Flat (球面摊不平)](https://world.lapla.si/en/projection/): plate M15. A sphere cannot be flattened without distortion. Every map projection gives something up: area, angles, distance or straight lines. Markdown: [en](https://world.lapla.si/en/projection/index.html.md), [中文](https://world.lapla.si/zh/projection/index.html.md).
- [More Than One Parallel (平行线不止一条)](https://world.lapla.si/en/hyperbolic/): plate M16. Replace Euclid’s fifth postulate by “through a point off a line there is more than one parallel”, and you get a world just as consistent: triangles add up to less than 180°, and space grows exponentially. Markdown: [en](https://world.lapla.si/en/hyperbolic/index.html.md), [中文](https://world.lapla.si/zh/hyperbolic/index.html.md).
- [The Fourth Direction (第四个方向)](https://world.lapla.si/en/polytope/): plate M17. Four-dimensional space holds six regular polytopes. We cannot see them, only their slices and their shadows: a three-dimensional hyperplane passing through, or a projection into our space. Markdown: [en](https://world.lapla.si/en/polytope/index.html.md), [中文](https://world.lapla.si/zh/polytope/index.html.md).
- [A Line That Fills a Square (一条线填满正方形)](https://world.lapla.si/en/hilbert/): plate M18. A continuous curve can pass through every point of a square. In 1891 Hilbert drew how: split into four, then four again, without end. Markdown: [en](https://world.lapla.si/en/hilbert/index.html.md), [中文](https://world.lapla.si/zh/hilbert/index.html.md).
- [How Evidence Moves Belief (证据如何改变相信)](https://world.lapla.si/en/bayes/): plate M19. Start with how much you believe something, see some evidence, and change your belief by the weight of that evidence. Bayes’ theorem says exactly how: the posterior is proportional to the prior times the likelihood. Markdown: [en](https://world.lapla.si/en/bayes/index.html.md), [中文](https://world.lapla.si/zh/bayes/index.html.md).
- [Every Loop Holds a Rectangle (每个圈上都有长方形)](https://world.lapla.si/en/mobius/): plate M20. Every closed curve in the plane has four points that form a rectangle. The proof lifts the pairs of points on the curve into space, where they make a Möbius strip; the strip cannot lie flat, it has to pass through itself, and where it does is a rectangle. Markdown: [en](https://world.lapla.si/en/mobius/index.html.md), [中文](https://world.lapla.si/zh/mobius/index.html.md).
- [Patterns Drawn by Diffusion (扩散画出的斑纹)](https://world.lapla.si/en/turing/): plate M21. Two substances: one makes more of itself, the other holds it down, and the one that holds it down spreads faster. An even mixture then breaks into spots or stripes on its own, at a spacing the equations set. Markdown: [en](https://world.lapla.si/en/turing/index.html.md), [中文](https://world.lapla.si/zh/turing/index.html.md).
- [Life from a Table of Numbers (一张表里长出的生命)](https://world.lapla.si/en/particles/): plate M22. A few kinds of beads, and one number between every two kinds: pull or push. Make the table lopsided and Newton’s third law fails; the tank never settles again. Markdown: [en](https://world.lapla.si/en/particles/index.html.md), [中文](https://world.lapla.si/zh/particles/index.html.md).

## Technology / Classic Machines

- [Watt’s Steam Engine (瓦特的蒸汽机)](https://world.lapla.si/en/steam/): plate C01. An iron vessel standing in cold water saved most of the coal; two spinning balls taught the engine its own pace. Built in Birmingham in 1788, it stands at rest in London today. Markdown: [en](https://world.lapla.si/en/steam/index.html.md), [中文](https://world.lapla.si/zh/steam/index.html.md).
- [The SLR Camera (单反相机)](https://world.lapla.si/en/camera/): plate C02. While you frame, a mirror behind the lens sends the light up into a prism. Press the release and the mirror lifts; two cloth curtains cross the film one after the other. Markdown: [en](https://world.lapla.si/en/camera/index.html.md), [中文](https://world.lapla.si/zh/camera/index.html.md).
- [The Escapement (擒纵机构)](https://world.lapla.si/en/escapement/): plate C03. A spring or a falling weight, let go, gives up its energy all at once. The escapement lets it out in equal small steps, one per beat, timed by something that swings back and forth. Markdown: [en](https://world.lapla.si/en/escapement/index.html.md), [中文](https://world.lapla.si/zh/escapement/index.html.md).
- [The Four-Stroke Engine (四冲程发动机)](https://world.lapla.si/en/engine/): plate C04. The fuel burns inside the cylinder. The piston makes four strokes and the crank turns twice; in one of them, the burning gas drives the piston down. Markdown: [en](https://world.lapla.si/en/engine/index.html.md), [中文](https://world.lapla.si/zh/engine/index.html.md).
- [The Printing Press (活字印刷机)](https://world.lapla.si/en/press/): plate C05. Metal letters set into a page, inked, covered with paper, one pull of the bar: a printed page. Mainz, about 1450. Markdown: [en](https://world.lapla.si/en/press/index.html.md), [中文](https://world.lapla.si/zh/press/index.html.md).
- [The Phonograph and the Gramophone (留声机)](https://world.lapla.si/en/phonograph/): plate C06. Sound pushes a needle that cuts wiggles into a groove; a needle running back along the wiggles brings the sound back. The whole machine runs without electricity. Markdown: [en](https://world.lapla.si/en/phonograph/index.html.md), [中文](https://world.lapla.si/zh/phonograph/index.html.md).
- [The Typewriter (打字机)](https://world.lapla.si/en/typewriter/): plate C07. Press a key and a typebar swings up and strikes the paper through the ribbon; let go and the carriage steps one space to the left. Markdown: [en](https://world.lapla.si/en/typewriter/index.html.md), [中文](https://world.lapla.si/zh/typewriter/index.html.md).
- [The Lockstitch Sewing Machine (缝纫机与锁式线迹)](https://world.lapla.si/en/sewing/): plate C08. The needle takes a loop of thread under the cloth; the hook carries it round the bobbin case and over the lower thread, and the loop is drawn back into the cloth. One turn of the handwheel, one stitch. Markdown: [en](https://world.lapla.si/en/sewing/index.html.md), [中文](https://world.lapla.si/zh/sewing/index.html.md).
- [The Enigma Cipher Machine (恩尼格玛密码机)](https://world.lapla.si/en/enigma/): plate C09. Press a key and the rotors step first; the current runs through the plugboard, three rotors and a reflector and back, and another letter lights up. Markdown: [en](https://world.lapla.si/en/enigma/index.html.md), [中文](https://world.lapla.si/zh/enigma/index.html.md).
- [The Difference Engine (差分机)](https://world.lapla.si/en/difference/): plate C10. Tables of polynomials by addition alone: eight columns of figure wheels, each added to the next, one result per turn of the cycle, printed straight away. Markdown: [en](https://world.lapla.si/en/difference/index.html.md), [中文](https://world.lapla.si/zh/difference/index.html.md).
- [The Picture Tube (显像管电视机)](https://world.lapla.si/en/crt/): plate C11. A beam of electrons in a vacuum, pushed about by magnetic fields more than fifteen thousand lines a second, paints a picture on phosphor one spot at a time. Markdown: [en](https://world.lapla.si/en/crt/index.html.md), [中文](https://world.lapla.si/zh/crt/index.html.md).
- [The Antikythera Mechanism (安提基西拉机械)](https://world.lapla.si/en/antikythera/): plate C12. A box of bronze gears from more than two thousand years ago: turn the crank, and the Sun, the Moon, its phase, the calendar and the eclipse cycles all move on together. Markdown: [en](https://world.lapla.si/en/antikythera/index.html.md), [中文](https://world.lapla.si/zh/antikythera/index.html.md).
- [The Tide-Predicting Machine (潮汐预报机)](https://world.lapla.si/en/tide/): plate C13. A row of cranks, one wire and a pen: Kelvin’s machine added ten cosines together and drew a year of a port’s tides in four hours. Markdown: [en](https://world.lapla.si/en/tide/index.html.md), [中文](https://world.lapla.si/zh/tide/index.html.md).
- [The Wankel Rotary Engine (转子发动机)](https://world.lapla.si/en/wankel/): plate C14. A three-sided rotor goes round inside a waisted bore: three chambers work through the four strokes at once, with no pistons going up and down and no valves. Markdown: [en](https://world.lapla.si/en/wankel/index.html.md), [中文](https://world.lapla.si/zh/wankel/index.html.md).
- [The Mark I Perceptron (感知机)](https://world.lapla.si/en/perceptron/): plate C15. A machine that learned letters from examples: four hundred photocells to see, 512 randomly wired units in between, and motor-driven potentiometers to remember. Markdown: [en](https://world.lapla.si/en/perceptron/index.html.md), [中文](https://world.lapla.si/zh/perceptron/index.html.md).

## Technology / Energy, Flight & Sensing

- [Five-Axis Machining Centre (五轴加工中心)](https://world.lapla.si/en/cnc/): plate F02. Three straight axes move the spindle, two rotary axes turn the part, and all five move together to cut an impeller from a solid block of aluminium. Markdown: [en](https://world.lapla.si/en/cnc/index.html.md), [中文](https://world.lapla.si/zh/cnc/index.html.md).
- [Tokamak Fusion Reactor (托卡马克聚变装置)](https://world.lapla.si/en/tokamak/): plate F06. A tokamak like ITER: eighteen D-shaped superconducting coils round a ring-shaped vacuum vessel, inside which a deuterium–tritium plasma at about 150 million degrees hangs in a magnetic field. Markdown: [en](https://world.lapla.si/en/tokamak/index.html.md), [中文](https://world.lapla.si/zh/tokamak/index.html.md).
- [Turbofan Engine (涡扇发动机)](https://world.lapla.si/en/turbofan/): plate F07. A high-bypass turbofan of the kind under a widebody’s wing, a quarter cut away: fan, ten-stage high-pressure compressor, annular combustor, two turbines. At take-off it swallows about 1.2 tonnes of air a second. Markdown: [en](https://world.lapla.si/en/turbofan/index.html.md), [中文](https://world.lapla.si/zh/turbofan/index.html.md).
- [The Gravitational-Wave Interferometer (引力波干涉仪)](https://world.lapla.si/en/ligo/): plate F08. Two arms 4 km long measure changes in length more than ten thousand times smaller than a proton. In 2015 it recorded, for the first time, the gravitational waves from two black holes merging. Markdown: [en](https://world.lapla.si/en/ligo/index.html.md), [中文](https://world.lapla.si/zh/ligo/index.html.md).
- [The Webb Space Telescope (韦布空间望远镜)](https://world.lapla.si/en/webb/): plate F09. Eighteen gold-coated segments make one 6.5 m mirror, and five layers of film keep the Sun’s heat off it. It was launched folded and unfolded itself in space over two weeks. Markdown: [en](https://world.lapla.si/en/webb/index.html.md), [中文](https://world.lapla.si/zh/webb/index.html.md).
- [The Harmonic Drive (谐波减速器)](https://world.lapla.si/en/harmonic/): plate F10. The strain-wave gear inside a robot joint: an ellipse flexes a thin steel cup, and each turn the cup falls back just two teeth. A 100 : 1 reduction in one stage, with almost no backlash. Markdown: [en](https://world.lapla.si/en/harmonic/index.html.md), [中文](https://world.lapla.si/zh/harmonic/index.html.md).
- [Lidar (激光雷达)](https://world.lapla.si/en/lidar/): plate F11. A lidar on a car’s roof times light: 6.67 nanoseconds there and back is one metre. 128 beams spin, and the street around turns into hundreds of thousands of points with coordinates. Markdown: [en](https://world.lapla.si/en/lidar/index.html.md), [中文](https://world.lapla.si/zh/lidar/index.html.md).
- [The Phased Array (相控阵：不转的天线)](https://world.lapla.si/en/phased/): plate F12. A flat panel holds a thousand small antennas. Let each send a moment after its neighbour and the beam leans to one side. No motor: the direction is set by timing alone. Markdown: [en](https://world.lapla.si/en/phased/index.html.md), [中文](https://world.lapla.si/zh/phased/index.html.md).