2c:null 2d:["$","title",null,{"children":"Quantum Glitching the Conway's Game of Life | rix | Observable"}] 32:T440,viewof lang = { const $ = html`

`; const langs = { en: { name: 'English', style: 'font-family: var(--serif) !important;' }, 'zh-CN': { name: '简体中文', style: 'font-family: var(--hans) !important;' }, }; const style = html``; $.appendChild(style); for (const [ code, lang ] of Object.entries(langs)) { lang.code = code; lang.link = html`${lang.name}`; lang.link.style = lang.style; $.appendChild(lang.link); lang.link.addEventListener('click', e => { e.stopPropagation(); if ($.value !== code) { select(code); $.dispatchEvent(new Event('input', { bubbles: true })); } }); } function select(code) { if ($.value) { langs[$.value].link.classList.remove('selected'); } $.value = code; localStorage.setItem('lang', code); style.innerHTML = `html, label, button, table { ${langs[code].style || ''} }`; langs[code].link.classList.add('selected'); } select(localStorage.getItem('lang') || 'en'); return $; }33:Te92,{ if (lang === 'en') return md` At the top of the screen it said > ${GameOfLifeTitle(last.t)}. So you figured what happened. The enemy were here a while ago, and he received an order written on this terminal. Probably encoded as some meaningful pattern in this [Game of Life](https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life) program. After reading the message, the enemy fast forwarded the game into a later generation, where the message was scrambled into meaningless patterns. The \`t=${last.t}\` mark on the screen means the program has executed ${last.t} generations. _OK._ You think, _maybe I could just **time-travel** back to when the message was still on the screen._ Yes, as a secret agent with top clearance level, you were equipped with the most alien device in the world - a portable **Time Machine**. You took out your pad - and yes, it's even as portable as a normal pad. You entered a timestamp of 2 hours ago, which you know was just before the enemy were here. And you initiated time travel. > \`FAILURE: TIME SPACE INSTABLE! QUANTUM JAMMER DETECTED!\` _Damn it!_ The enemy knew you could do time travel. They protected this place with quantum jammer to prevent you entering from the past. This is not good news. _Maybe there's another way._ You started to think very hard. Although human flesh like yourself cannot be portaled to the past, maybe something smaller could? Maybe ... **electrons**? You pressed a button on your pad, and it transformed into a hand gun! It's now a gun that can shoot electromagnetic waves to the past. You aimed it at the terminal, and fired. The space around that terminal screen seemed to be twisted. It's the quantum effect taking place, altering the reality as you watched. Suddenly the screen flashed, and the pattern on it has changed a little bit. `; if (lang === 'zh-CN') return md` 在屏幕的上方显示着一行字 > ${GameOfLifeTitle(last.t)}. 你大概明白了事情的经过。敌人在不久前还在这个房间，他从这台终端上接收到了一份指令。指令大概是以带有含义的图案画在了这个 [生命游戏 (Game of Life)](https://zh.wikipedia.org/wiki/%E5%BA%B7%E5%A8%81%E7%94%9F%E5%91%BD%E6%B8%B8%E6%88%8F) 的程序中。在阅读了信息后，敌人执行了游戏的迭代指令，原本的信息被混淆成了你现在看到的混乱的图案。屏幕上的 \`t=${last.t}\` 标识说明程序迭代了 ${last.t} 次。 _好吧。_你想到，_也许我可以时空穿越到屏幕上还显示着有用信息的那个时间点。_是的，作为拥有最高保密级别的特工，你随身携带着这个世界上最黑科技的装置——便携式的**时间机器**。你拿出了你的平板——没错，它的便携程度跟一个普通平板一样。你输入了 2 小时之前的一个时间值，你知道在那个时间敌人还没有来到这里。你尝试执行时空穿越。 > **_错误：时空不稳定！检测到量子干涉器！_** 该死！狡猾的敌人知道你可以穿越时空。他们设下了量子干涉器阻止你从过去进入这个房间。这可不是什么好事。 _也许还有什么别的办法。_你开始飞速思考。虽然人体无法突破敌人的屏障穿越时空，但是质量小点的东西也许可以。也许…… **电子** 可以？你按下了平板上的一个键，顿时平板开始了形变，居然变成了一把手枪！现在它是一把能向过去发射电磁波的手枪。你瞄准眼前的终端，扣动了扳机。屏幕周围的空间扭曲了起来。这正是量子效应发生时的景象，你所处的现实正在你的观察下被改变着。忽然间屏幕闪烁了一下，屏幕上的图案有了些许变化。 `; } 34:T1164,{ if (lang === 'en') return md` _It works!_ You were amazed by the result. There's a crack in the enemy's quantum firewall - you can send electromagnetic waves to the past to glitch the terminal! Electronic chips are prone to EM-wave interference and by hitting it with a large amount of them you managed to flip bits inside it. And it happened in the past. You were able to perform **[Fault Injection Attacks](https://en.wikipedia.org/wiki/Fault_injection) on the program through time!** _I can probably exploit this weakness to read the message on the screen at \`t=0\`._ You were on to something. You did some tuning of the time travel electromagnetic hand gun, now you were able to accurately flip bits at any \`t\` generation of this Game of Life program. Every such bit flipped would cause a cell on screen being flipped as well at that point in time. That cell flip would be propagated to your current time and you would see the glitched result at \`t=${last.t}\` on the screen in front of you. There's also a button on your hand gun to reset all the glitches to return the program to its original state. If you could solve the original pattern at \`t=${last.t-1}\`, you would be able to use it to [get past the enemy's quantum firewall](#breachQuantumFirewall) a little bit more, and you would be able to observe the glitched \`t=${last.t-1}\` result directly on your pad. Let's try with an example. Below is an interactive demonstration of how the time-travel glitching attack works. Although on a small board but all the hidden underlying states are revealed. Every row represents the states of the Game of Life at \`t\` generation. The first column represents the starting input state of the board at that generation. For all ${tex`t > 0`}, the input state is just the output state from the \`t-1\` generation. The second column represents the cells you would like to flip. The third column shows you the glitched input state after applying your flips. The last column show you the Game of Life output on the glitched state of that generation. You can click to edit the initial input at \`t=0\`, and every flips at any point in time. Please observe how the glitches propagate through time. `; if (lang === 'zh-CN') return md` _成了！_你对这个结果感到了激动。敌人的量子防火墙存在一条裂缝——你可以向过去发射电磁波对这台终端进行故障攻击！电子芯片在受到电磁波干扰的情况下容易造成内部数位比特 (bits) 的反转。而且这种反转发生在过去。你可以对这个程序进行 **跨越时空的 [故障攻击 (Fault Injection Attack)](https://en.wikipedia.org/wiki/Fault_injection)！** _我也许可以利用这个弱点读取到在 \`t=0\` 时间点屏幕上面的信息。_你找到了一个突破口。你对这把时空电磁枪进行了微调，现在你可以精准地朝任何 \`t\` 时间点发射精确控制的电磁波，准确的反转这个生命游戏中你想要反转的数位 bits。被反转的数位 bit 会同时造成那个时间点上屏幕上的对应格子也被反转。被反转的格子会影响原本程序迭代的状态，处于当下的你会在眼前的屏幕上看到被扭曲时空影响后的 \`t=${last.t}\` 迭代的状态。你的时空电磁枪上还有一个按钮可以重置一切时空影响，将程序重置回去原本时空的状态。如果你能解出第 \`t=${last.t-1}\` 迭代的原本状态，你就能以此作为时空锚点进一步[突破敌人设下的时空屏障](#breachQuantumFirewall)，能够直接在你的平板上观察被时空扭曲后影响的 \`t=${last.t-1}\` 的状态。来尝试一个演示吧。下面是这个时空故障攻击原理的交互式演示。虽然用的是一个小的盘面，但是所有隐藏的内部状态都向你展示了。每一行表示在一轮 \`t\` 迭代时间上生命游戏盘面的状态。第一列表示该迭代的输入状态。对于所有 ${tex`t > 0`} 的迭代，输入的盘面就是上一轮迭代 \`t-1\` 中的输出。第二列表示你想要反转的格子。第三列表示输入盘面在反转了你想要反转的格子后的状态。最后一列表示对被反转后的输入执行生命游戏的迭代计算后的输出。你可以点击编辑 \`t=0\` 迭代的初始输入，也可以编辑任何迭代中你想要反转的格子。请观察反转造成的故障是如何迭代影响到后面的时间线的。 `; }35:T777,{ const numFrames = 4; const timeline = []; for (let t = 0; t < numFrames; t++) { let input, flips, flipped, output; if (t === 0) { input = Board(fromAscii( `░░░░░`, `░██░░`, `░░██░`, `░░██░`, `░░░░░`, ), { editable: true }); watch(input); flips = Board(fromAscii( `░░░░░`, `░██░░`, `░░░█░`, `░█░░░`, `░░░░░`, ), { editable: true }); } else { input = Board(timeline[t-1].output.value); flips = Board(fromAscii( `░░░░░`, `░░░░░`, `░░░░░`, `░░░░░`, `░░░░░`, ), { editable: true }); } watch(flips); flipped = Board(flipBoard(input.value, flips.value)); output = Board(nextGeneration(flipped.value)); timeline.push({ t, input, flips, flipped, output }); } function watch(board) { d3.select(board).on('input', update); } function update() { for (let t = 0; t < numFrames; t++) { const { input, flips, flipped, output } = timeline[t]; if (t > 0) input.value = timeline[t-1].output.value; flipped.value = flipBoard(input.value, flips.value); output.value = nextGeneration(flipped.value); } } const table = d3.create('table'); table.selectAll('tr') .data(timeline) .join('tr') .selectAll('td') .data(d => [html`t=${d.t}`, d.input, d.flips, d.flipped, d.output]) .join('td') .insert(d => d); table .insert('tr', 'tr') .selectAll('th') .data({ en: ['', 'Input', 'Flips', 'Flipped Input', 'Output'], 'zh-CN': ['', '输入', '反转', '反转后的输入', '输出'], }[lang]) .join('th') .text(d => d); return table.node(); }36:T8e4,{ if (lang === 'en') return md` ---- ## How to use the API At some point you probably need to write a program to solve this puzzle. Here is the description of how to use the API endpoint to perform the glitching attack. \`\`\` POST ${API_URL} Request JSON: { glitch: Timeline, // faults you want to inject solved: Timeline // generations you solved } Response JSON: { result: Timeline // generations observed } Timeline Object: { 14: [ // generation 14 [1,0,1,0,1,0,0,1,1], // 1 for active cell [1,0,1,0,1,0,0,1,1], // 0 for inactive cell [1,0,1,0,1,0,0,1,1], // one array per row [1,0,1,0,1,0,0,1,1], // and all rows in an array [1,0,1,0,1,0,0,1,1], [1,0,1,0,1,0,0,1,1], ] } \`\`\` A succesfully solved generation \`t\` would allow you to observe glitched state at \`t\` when you specify glitches at \`t-1\`. So to verify your solution for \`t\`, include it in the solved Timeline. If it's correct, you should see \`t\` states being included in the result Timeline as response. When you see \`t=0\` in the result timeline, you have fully solved the puzzle. `; if (lang === 'zh-CN') return md` ---- ## 如何调用 API 请求在某个阶段你可能需要编写程序来解决这个谜题。下面给出了使用 API 请求执行故障攻击的方法。 \`\`\` POST ${API_URL} Request JSON: { glitch: Timeline, // 你想要注入的故障 solved: Timeline // 你已经解出来的迭代 } Response JSON: { result: Timeline // 观测到的迭代 } Timeline Object: { 14: [ // 第 14 次迭代 [1,0,1,0,1,0,0,1,1], // 1 代表黑格子 [1,0,1,0,1,0,0,1,1], // 0 代表白格子 [1,0,1,0,1,0,0,1,1], // 每行一个数组 [1,0,1,0,1,0,0,1,1], // 全部行放在一个数组中 [1,0,1,0,1,0,0,1,1], [1,0,1,0,1,0,0,1,1], ] } \`\`\` 如果你正确解出了一个 \`t\` 迭代，你将获得观察受 \`t-1\` 故障影响后的 \`t\` 的状态。要验证你对 \`t\` 迭代的解，只需要将它写在 solved 字段中。如果你的解正确，你就会在 result 字段中看到 \`t\` 迭代的状态。当你看到 \`t=0\` 迭代出现在 result 字段中时，你就成功地解开了这个谜题。 `; }37:Td36,{ if (lang === 'en') return md` ----

Need some tips

For any cell on row ${tex`r`} and column ${tex`c`} at generation ${tex`t+1`}, denoted as ${tex`C_{r,c,t+1}`}. Its value depends on the surrounding 8 cells and itself at ${tex`t`}. We denote the cells ${tex`C_{r,c,t}`} depends on as a block ${tex`B_{r,c,t+1}=\begin{Bmatrix} C_{r-1,c-1,t} & C_{r-1,c,t} & C_{r-1,c+1,t} \\ C_{r,c-1,t} & C_{r,c,t} & C_{r,c+1,t} \\ C_{r+1,c-1,t} & C_{r+1,c,t} & C_{r+1,c+1,t} \end{Bmatrix}`}. Then we can express

${tex`C_{r,c,t+1} = Gen(B_{r,c,t}) = \begin{cases} 1 & \text{if } Sum(B_{r,c,t})-C_{r,c,t} = 3 \text{ or } ( Sum(B_{r,c,t})-C_{r,c,t} = 2 \text{ and } C_{r,c,t} = 1 ) \\ 0 & \text{otherwise} \end{cases} `}

Our ability is to observe ${tex`C_{r,c,t+1}' = Gen(B_{r,c,t}')`} while modifying ${tex`B_{r,c,t}'=B_{r,c,t} \oplus F`} with ${tex`F`} being a fault that we control. But we cannot directly observe ${tex`B_{r,c,t}'`} or ${tex`B_{r,c,t}`}. The idea is if we can repeatly inject different faults ${tex`F`}, we would be able to build a look-up table for the function ${tex`Gen'(B_{r,c,t},F)=Gen(B_{r,c,t} \oplus F)`} for a full domain of ${tex`F`}. Then if we brute-force every ${tex`B`} we can find the block that would produce the same look-up table for ${tex`Gen'(B_{r,c,t},F)`}, and that ${tex`B`} is the solution to ${tex`B_{r,c,t}`}.

This is the fundamental principle for solving this puzzle, but try to come up with an implementation, and optimize it to efficiently solve the puzzle.

`; if (lang === 'zh-CN') return md` ----

需要提示吗

对于一个在 ${tex`r`} 行 ${tex`c`} 列，第 ${tex`t+1`} 次迭代的格子，我们记为 ${tex`C_{r,c,t+1}`}。它的值依赖于第 ${tex`t`} 次迭代的周围八个格子和它自己。我们把${tex`C_{r,c,t+1}`} 依赖的格子记为一个块 ${tex`B_{r,c,t+1}=\begin{Bmatrix} C_{r-1,c-1,t} & C_{r-1,c,t} & C_{r-1,c+1,t} \\ C_{r,c-1,t} & C_{r,c,t} & C_{r,c+1,t} \\ C_{r+1,c-1,t} & C_{r+1,c,t} & C_{r+1,c+1,t} \end{Bmatrix}`}。然后我们可以表示

我们的能力是可以用一个可控的故障 ${tex`F`} 来改动 ${tex`B_{r,c,t}'=B_{r,c,t} \oplus F`} 并观测输出结果 ${tex`C_{r,c,t+1}' = Gen(B_{r,c,t}')`}。但是我们无法直接观测 ${tex`B_{r,c,t}'`} 或者 ${tex`B_{r,c,t}`}。主要的思路是通过重复注入不同的故障 ${tex`F`}，我们可以对完整的 ${tex`F`} 值域建立一个对函数 ${tex`Gen'(B_{r,c,t},F)=Gen(B_{r,c,t} \oplus F)`} 的查找表。然后如果我们暴力尝试所有可能的 ${tex`B`} 的值，我们就能找到一个块可以生成和 ${tex`Gen'(B_{r,c,t},F)`} 一样的查找表，而这个 ${tex`B`} 就是 ${tex`B_{r,c,t}`} 的答案。

这是解决这道谜题的基本思路，还请你尝试实现并优化一个方法能高效地解开这个谜题。

`; }38:T81e,Ending = { if (first.t > 0) { if (lang === 'en') return md` ---- ## Status: Still on going Your progress is at \`t=${first.t}\`. Please carry on! `; if (lang === 'zh-CN') return md` ---- ## 进度：破译还未完成你当前破译的进度为 \`t=${first.t}\`。请再接再厉！ `; } else { if (lang === 'en') return md` ---- ## You did it! ${Frame(first, { title: GameOfLifeTitle })} You successfully cracked the original message. It seems even quantum firewall were nothing special. It couldn't stop you at all. The enemy's target has been revealed, and it's crucial to report it immediately. You swiftly left the room, but just as you were about to send a message to your handler, a deafening blast echoed from behind you. Before you could even turn around, a wave of heat had already engulfed you - it was an explosion. The enemy discovered your breakthrough in their quantum defenses and now trying to wipe your existence. There's no time to evade the shockwave, but at least you need to preserve this one thing. In the midst of the crisis, you tossed the tablet containing enemy intelligence away. In the next instant, you were consumed by light and heat, and all perception gradually faded away... (To be coninuted...) `; if (lang === 'zh-CN') return md` ---- ## 破译成功！ ${Frame(first, { title: GameOfLifeTitle })} 你成功地分析出了原始的信息，看来所谓的量子干扰手段也不过如此，完全难不倒你。敌人的目标原来是这个，需要马上向组织汇报。你迅速离开了房间，然而正当你要向上级发送信息的时候，一声巨响从你身后传来，还未来得及回头，一股热浪已经将你席卷——是爆炸。敌人发现了你突破他们量子防护的攻击，现在正要将你彻底清除。已经来不及避开冲击波了，但是至少这个要保住。危机之中，你把记载着敌人情报的平板丢了出去，接下来的一瞬间你便被光和热吞噬，一切知觉都逐渐地远去…… （有缘待续） `; } }39:Td93,function Board(board, option = {}) { let radius = option.radius || 20; let editable = !!option.editable; const container = d3.create('div') .classed('board', true); const $ = container.node(); const svg = container.append('svg'); const overlay = container.append('div') .classed('overlay hidden', true); const input = overlay.append('textarea') .attr('placeholder', { en: 'Please enter the board:', 'zh-CN': '请输入盘面：', }[lang]) .classed('input', true) .on('keypress', function (e) { if (e.code === 'Enter') { const newBoard = fromAscii(this.value); if (newBoard) { const _dimension = dimension(board); const newDimension = dimension(newBoard); if (_dimension.width === newDimension.width && _dimension.height === newDimension.height) { set(newBoard); $.dispatchEvent(new Event('input', { bubbles: true })); } } this.value = ''; overlay.classed('hidden', true); } }); const controls = container.append('div') .classed('controls', true); const paste = controls.append('i') .attr('title', { en: 'Paste', 'zh-CN': '粘贴', }[lang]) .classed('btn fa-regular fa-paste', true) .on('click', () => { const input$ = input.node(); input$.value = ''; overlay.classed('hidden', false); input$.focus(); }); const copy = controls.append('i') .attr('title', { en: 'Copy', 'zh-CN': '复制', }[lang]) .classed('btn fa-solid fa-copy', true) .on('click', () => { navigator.clipboard.writeText(toAscii(board).join('\n')); }); function cellColor(x, y) { return board[y][x] ? 'block' : 'white'; } function flipCell(x, y) { board[y][x] = board[y][x] ? 0 : 1; } function renderSVG() { const { width, height } = dimension(board); svg .attr('width', width * radius + 1) .attr('height', height * radius + 1) .attr('viewBox', [-0.5, -0.5, width * radius + 1, height * radius + 1]) .attr('stroke', 'lightgray') .selectAll('g') .data(board) .join('g') .selectAll('rect') .data((row, y) => row.map((_, x) => ({ x, y }))) .join('rect') .attr('width', radius) .attr('height', radius) .attr('x', ({ x }) => x * radius) .attr('y', ({ y }) => y * radius) .attr('fill', ({ x, y }) => cellColor(x, y)); if (editable) { paste.classed('hidden', false); svg.selectAll('rect') .on('mouseover', function() { d3.select(this).attr('fill', 'red'); }) .on('mouseout', function() { d3.select(this).attr('fill', ({ x, y }) => cellColor(x, y)) }) .on('click', function() { const { x, y } = d3.select(this).datum(); flipCell(x, y); $.dispatchEvent(new Event('input', { bubbles: true })); }); } else { paste.classed('hidden', true); svg.selectAll('rect') .on('mouseover', null) .on('mouseout', null) .on('click', null); } } function set(value) { board = value; renderSVG(); } function get() { return board; } renderSVG(); Object.defineProperty($, 'value', { get, set }); Object.defineProperty($, 'radius', { set(value) { radius = value; renderSVG(); } }); Object.defineProperty($, 'editable', { set(value) { editable = !!value; renderSVG(); } }); return $; }3a:Tac4,function Frame(frame, option = {}) { /* ╭― container ―――――――――――╮ │╭― header ――――――――――――╮│ ││╭― title ―――――――――――╮││ ││╰―――――――――――――――――――╯││ │╰―――――――――――――――――――――╯│ │╭― body ――――――――――――――╮| |│╭― board――――――――――――╮│| ││| |│| ││| |│| ││| |│| ││| |│| ││| |│| ││╰―――――――――――――――――――╯│| │╰―――――――――――――――――――――╯│ ╰―――――――――――――――――――――――╯ */ const container = d3.create('div') .classed('frame', true); const $ = container.node(); const header = container.append('div') .classed('header', true); let { title } = option; const title$ = header.append('div') .classed('title', true); function renderTitle() { title$.selectChildren('*').remove(); if (_.isFunction(title)) { const el = title(frame); if (el) { title$.append(() => el); } } } renderTitle(); const body = container.append('div') .classed('body', true); const board = Board(frame.board, option); body.append(() => board); let { overlay } = option; const overlay$ = body.append('div') .classed('overlay', true); function renderOverlay() { overlay$.selectChildren('*').remove(); if (_.isFunction(overlay)) { const el = overlay(frame); if (el) { overlay$ .classed('hidden', false) .append(() => el); return; } } overlay$.classed('hidden', true); } renderOverlay(); // event -> board // ↓ // frame -> event // ↓ // bubbles -> event board.addEventListener('input', () => { frame = { t: frame.t, board: board.value }; }); // board -> value // ↑ // value -> frame function set(value) { frame = value; board.value = frame.board; renderTitle(); renderOverlay(); } // frame -> value function get() { return frame; } Object.defineProperty($, 'value', { get, set }); Object.defineProperty($, 'editable', { set(value) { board.editable = value; } }); Object.defineProperty($, 'title', { set(value) { title = value; renderTitle(); } }); Object.defineProperty($, 'overlay', { set(value) { overlay = value; renderOverlay(); } }); return $; }3b:Ta76,async function Timeline(timeline, option = {}) { const { localStorageName, load, range, initT, label, overlay } = option; let _dimension = option.dimension; option.overlay = wrapOverlay(overlay); const container = d3.create('div') .classed('timeline', true); const $ = container.node(); async function initLoad() { if (timeline) return; if (localStorageName) { const item = localStorage.getItem(localStorageName); if (item) return void(timeline = objectToSparse(JSON.parse(item))); } if (_.isFunction(load)) { return void(timeline = await load()); } timeline = []; } await initLoad(); if (!_dimension && timeline) { const first = firstFrame(timeline); _dimension = dimension(first.board); } function store() { if (localStorageName) { localStorage.setItem(localStorageName, JSON.stringify(sparseToObject(timeline))); } } function getRange() { if (_.isFunction(range)) { return range(timeline); } const last = lastFrame(timeline); return [0, last.t]; } function getInitT() { if (_.isFunction(initT)) { return initT(timeline); } const last = lastFrame(timeline); return last.t; } function getLabel() { if (_.isFunction(label)) { return label(timeline); } return html`${{ en: 'Generation', 'zh-CN': '迭代' }[lang]} t`; } function wrapOverlay(fn) { if (!_.isFunction(fn)) return fn; return frame => fn(frame, timeline); } const slider = Inputs.range(getRange(), { value: getInitT(), step: 1, label: getLabel() }); container .append(() => slider) .classed('slider', true) .on('input', e => { e.stopPropagation(); renderFrame(); }); const frame = Frame(frameAt(timeline, slider.value, _dimension), option); container .append(() => frame) .classed('frame', true) .on('input', onFrameChanged); function onFrameChanged() { const { t, board } = frame.value; if (isEmpty(board)) { delete timeline[t]; } else { timeline[t] = board; } store(); } function renderFrame() { frame.value = frameAt(timeline, slider.value, _dimension); } function set(value) { timeline = value; store(); renderFrame(); } function get() { return timeline; } Object.defineProperty($, 'value', { get, set }); Object.defineProperty($, 'title', { set(value) { frame.title = value; } }); Object.defineProperty($, 'overlay', { set(value) { frame.overlay = wrapOverlay(value); } }); Object.defineProperty($, 'editable', { set(value) { frame.editable = value; } }); return $; }3c:T885,3d:[] 30:{"id":"b26758d625031333","slug":"game-of-life","title":"Quantum Glitching the Conway's Game of Life","thumbnail":"5d13d7380205bebeb64b44f3bc78f4293cf8ed97cad3e5909a4a2ef3f1b2f8ca","access_level":"public","create_time":"$D2023-05-28T21:55:52.631Z","update_time":"$D2023-05-31T06:53:47.092Z","view_time":null,"first_public_time":"$D2023-05-28T21:55:52.631Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"72e51317eb10aec3","login":"rix","name":"rix","avatar_url":"https://avatars-next.observableusercontent.com/20058f5572c00c2807c8c0a31d6dc913ee57ddabc4e75869a4666632e88b7fa3","tier":"starter_2024","bio":""},"version":1427,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"ddedbb681d4376e1","login":"rix","name":"rix","avatar_url":"https://avatars-next.observableusercontent.com/20058f5572c00c2807c8c0a31d6dc913ee57ddabc4e75869a4666632e88b7fa3","tier":null,"bio":""}],"members":[{"type":"individual","id":"ddedbb681d4376e1","login":"rix","name":"rix","avatar_url":"https://avatars-next.observableusercontent.com/20058f5572c00c2807c8c0a31d6dc913ee57ddabc4e75869a4666632e88b7fa3","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Quantum Glitching the Conway's Game of Life","cells":[{"id":0,"value":"{\n if (lang === 'en') return md`\n# Quantum Glitching the Conway's Game of Life\n## A puzzle game introduction to [Differential Fault Analysis](https://en.wikipedia.org/wiki/Differential_fault_analysis) attack\n`;\n if (lang === 'zh-CN') return md`\n# 量子漩涡中的生命游戏\n## 以解谜的方式介绍 [差分故障分析 (Differential Fault Analysis)](https://zh.wikipedia.org/wiki/%E5%B7%AE%E5%88%A5%E9%8C%AF%E8%AA%A4%E5%88%86%E6%9E%90) 攻击\n`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":616,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1299,"value":"{\n if (lang === 'en') return note(md`\n**Note**: Programing is required to successfully solve this puzzle.\n`);\n if (lang === 'zh-CN') return note(md`\n**注意**：解决这则谜题需要用到编程。\n`);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":170,"value":"{\n if (lang === 'en') return md`\nFollowing trails left by the enemy spy, you found this rendezvous point where he used to receive orders from. Located in the back of a retro-game center, a narrow stairwell led you to this secret room. No one was inside, but there's a terminal screen flashing dimmed light. You stepped closer. The screen was showing some random-like pattern of some kind of image.\n`;\n if (lang === 'zh-CN') return md`\n追寻着敌方间谍留下的蛛丝马迹，你终于找到了他从上级接收指令的接头地点。这是一个老旧游戏机厅后面的小巷，狭窄的楼梯间将你带向了这个秘密的房间。房间内没有人，但是一台终端正在黑暗中发出着暗淡的荧光。你走上前去。屏幕上显示着看起来像是胡乱涂鸦的图案。\n`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":172,"value":"Frame(last, { title: GameOfLifeTitle });","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":176,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":210,"value":"{\n const domain = [0, 10000];\n const scale = d3.scalePow(domain, [0, 1]).exponent(3);\n const chaos = Inputs.range(domain, {value: 3000, step: 1, label: {\n en: 'Interference Energe Level',\n 'zh-CN': '干扰能量级别',\n }[lang]});\n const last = lastFrame(viewof timeline.value); // decouple from timeline\n const { width, height } = dimension(last.board);\n const frame = Frame(last, { title: GameOfLifeTitle });\n async function render() {\n const flips = { [last.t-1]: randomBoard(width, height, scale(chaos.value))};\n frame.value = frameAt(await request([], flips), last.t);\n }\n render();\n d3.select(chaos).on('input', e => { e.stopPropagation(); render(); });\n return html`

${chaos}${frame}

`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":213,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":234,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":403,"value":"{\n if(lang === 'en')\n return md`\n----\n## Attack time\n\nGot a hang of it ug? Now, it's time to develop a real attack to find out the secret on the enemy's terminal at \\`t=0\\`! Arm your flips below and hit \"Attack\" to glitch the game through time.\n`;\n if(lang === 'zh-CN')\n return md`\n----\n## 攻击时间\n\n找到感觉了吗？现在是时候对敌人的终端进行实战的攻击破解在 \\`t=0\\` 迭代时屏幕上的信息了！准备好你想要反转的格子然后点击“攻击”执行时空故障攻击。\n`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":414,"value":"viewof flipsTimeline = await Timeline(null, {\n editable: true,\n localStorageName: 'flips',\n dimension: dimension(last.board),\n range: () => [0, last.t-1],\n initT: () => first.t-1,\n title: ({t}) => html`

${{\n    en: `Cells you want to flip at t=${t} generation`,\n    'zh-CN': `你想在 t=${t} 迭代反转的格子`,\n  }[lang]}

`,\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":853,"value":"{\n const button = d3.create('button')\n .text({\n en: 'Attack!',\n 'zh-CN': '攻击！'\n }[lang])\n .on('click', attack);\n\n async function attack() {\n const resultTimeline = await request(viewof solvedTimeline.value, viewof flipsTimeline.value);\n viewof timeline.value = resultTimeline;\n viewof timeline.dispatchEvent(new Event('input', { bubbles: true }));\n if (resultTimeline[0]) {\n Ending.scrollIntoView();\n }\n }\n\n return button.node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":363,"value":"viewof timeline = await Timeline(null, {\n localStorageName: 'result',\n load: request,\n range: timeline => {\n const last = lastFrame(timeline);\n return [0, last.t];\n },\n initT: timeline => {\n const first = firstFrame(timeline);\n return first.t;\n },\n title: ({t}) => html`${{\n en: `Observed output at t=${t} generation`,\n 'zh-CN': `观测到的 t=${t} 迭代输出`,\n }[lang]}`,\n overlay: ({t}, timeline) => {\n if (timeline[t]) return;\n return {\n 'en': md`Observation failed due to quantum jamming!\\n\\nPlease solve the original state at \\`t=${t}\\` to [breach the enemy's quantum firewall!](#breachQuantumFirewall)`,\n 'zh-CN': md`受量子干扰，观测失败！\\n\\n请在解出原时空 \\`t=${t}\\` 状态之后 [突破敌人的时空屏障！](#breachQuantumFirewall)`,\n }[lang];\n },\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":731,"value":"breachQuantumFirewall = {\n if (lang === 'en')\n return md`\n----\n## Breaching the quantum firewall\nGreat! You have solved the original state of the game at some ${tex`t < ${last.t}`} generation? Using this information as a time-space anchor, you are able to create quantum function convergence in a higher dimension. Even though you still wouldn't be able to time travel to that time in person, you would be able to observe the glitched state of that generation leveraging the quantum entanglement effects. Enter the solved states below, and if you were correct, next time you perform a glitching attack through time, your pad would show you the glitched states of those solved generations.\n`;\n if (lang === 'zh-CN')\n return md`\n----\n## 突破时空屏障\n太好了！你解出了某个 ${tex`t < ${last.t}`} 迭代的原始状态吗？你可以利用这个信息作为时空锚点，在高维空间中制造量子函数的坍缩。即使你仍然无法肉身穿越到这个时间点，但是你现在可以通过量子纠缠效应测算出来这个迭代被时空故障影响扭曲后的状态。在下面这个程序中添加你已经解出来的迭代锚点，如果正确，在你下次执行时空故障攻击时，你的平板应该就能告诉你所有解出的迭代被影响后的状态了。\n`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":775,"value":"viewof solvedTimeline = await Timeline(null, {\n editable: true,\n localStorageName: 'solved',\n dimension: dimension(last.board),\n range: () => [0, last.t-1],\n initT: () => first.t-1,\n title: ({t}) => html`${{\n en: `Your solution to t=${t}`,\n 'zh-CN': `你解出的 t=${t}`,\n }[lang]}`,\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1307,"value":"{\n if (lang === 'en') return note(md`\n**Note**: After solving \\`t=0\\`, you need to perform a glitching attack again to verify your solution. If you were correct, you would be sent to the ending scene.\n`);\n if (lang === 'zh-CN') return note(md`\n**注意**：在破译了 \\`t=0\\` 之后，你需要再执行一次攻击来验证你的答案。如果你的答案正确，你会被带到结局情节。\n`);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1398,"value":"$36","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1409,"value":"{\n if (lang === 'en') return note(md`\n**Note**: Please avoid bruf-forcing the API endpoint.\n`);\n if (lang === 'zh-CN') return note(md`\n**注意**：请不要暴力请求 API 节点。\n`);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1292,"value":"$37","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":988,"value":"$38","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"{\n if (lang === 'en')\n return md`\n----\n## Appendix\n`;\n if (lang === 'zh-CN')\n return md`\n----\n## 附加代码\n`;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":978,"value":"{\n return d3.create('button')\n .text({\n en: 'Clear local storage',\n 'zh-CN': '清除本地数据',\n }[lang])\n .on('click', () => {\n localStorage.clear();\n })\n .node();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"$39","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1020,"value":"$3a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1064,"value":"$3b","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":53,"value":"function table(width, height, fill = 0) {\n const t = new Array(height);\n for (let i = 0; i < height; i++) t[i] = new Array(width).fill(fill);\n return t;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"function fromAscii(...rows) {\n rows = rows.join('\\n').split('\\n').filter(l=>l);\n if (rows.length === 0) return;\n return rows.map((r) => Array.from(r).map((c) => (c === '░' ? 0 : 1)));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":146,"value":"function toAscii(board) {\n return board.map(row => row.map(c => c ? '█' : '░').join(''));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":459,"value":"function dimension(board) {\n const height = board.length;\n const width = board[0].length;\n return { width, height };\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":281,"value":"function nextGeneration(board) {\n const { width, height } = dimension(board);\n function sumNeighbors(row, col) {\n let sum = 0;\n if (row > 0) {\n if (col > 0) {\n sum += board[row - 1][col - 1];\n }\n sum += board[row - 1][col];\n if (col < width - 1) {\n sum += board[row - 1][col + 1];\n }\n }\n if (col > 0) {\n sum += board[row][col - 1];\n }\n if (col < width - 1) {\n sum += board[row][col + 1];\n }\n if (row < height - 1) {\n if (col > 0) {\n sum += board[row + 1][col - 1];\n }\n sum += board[row + 1][col];\n if (col < width - 1) {\n sum += board[row + 1][col + 1];\n }\n }\n return sum;\n }\n return board.map((r, row) =>\n r.map((c, col) => {\n const sum = sumNeighbors(row, col);\n if (sum === 3 || (c === 1 && sum === 2)) {\n return 1;\n }\n return 0;\n })\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":298,"value":"function flipBoard(board, flip) {\n return board.map((r, row) =>\n r.map((c, col) => {\n return c ^ flip[row][col];\n })\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":368,"value":"function firstFrame(timeline) {\n let first;\n for (let t in timeline) {\n if (timeline[t]) {\n first = { t, board: timeline[t] };\n break;\n }\n }\n return first;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":371,"value":"function lastFrame(timeline) {\n let last;\n for (let t = timeline.length-1; t >= 0; t--) {\n if (timeline[t]) {\n last = { t, board: timeline[t] };\n break;\n }\n }\n return last;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1099,"value":"function frameAt(timeline, t, dimension) {\n if (timeline[t]) return { t, board: timeline[t] };\n if (dimension) {\n const { width, height } = dimension;\n return { t, board: table(width, height, 0) };\n }\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1083,"value":"first = firstFrame(timeline)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1085,"value":"last = lastFrame(timeline)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":360,"value":"async function request(solved, glitch) {\n solved = sparseToObject(solved);\n glitch = sparseToObject(glitch);\n const { result } = await (await fetch(API_URL, { method: 'POST', body: JSON.stringify({ solved, glitch }) })).json();\n return objectToSparse(result);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":590,"value":"function isEmpty(board) {\n if (!board) return true;\n return !board.some(row => row.some(c => c));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":562,"value":"function GameOfLifeTitle({t}) {\n return html`Conway's Game of Life, t=${t}.`\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":454,"value":"function randomBoard(width, height, chaos = 0.01) {\n const board = table(width, height);\n for (let r = 0; r < height; r++) {\n for (let c = 0; c < width; c++) {\n board[r][c] = Math.random() < chaos ? 1 : 0;\n }\n }\n return board;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":351,"value":"API_URL = 'https://game-of-life.metacoder.workers.dev/TimeTravelGlitch'","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1121,"value":"function sparseToObject(sparse) {\n if (!_.isArray(sparse)) return sparse;\n const obj = {};\n for (let k in sparse) {\n obj[k] = sparse[k];\n }\n return obj;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1123,"value":"function objectToSparse(obj) {\n if (_.isArray(obj)) return obj;\n const sparse = [];\n for (const [k, v] of Object.entries(obj)) {\n sparse[k] = v;\n }\n return sparse;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":483,"value":"{\n const domain = [0, 10000];\n const scale = d3.scalePow(domain, [0, 1]).exponent(3);\n const chaos = Inputs.range(domain, {value: 3000, step: 1, label: \"Chaos\"});\n const { width, height } = dimension(lastFrame(timeline).board);\n const board = Board(randomBoard(width, height, chaos.value));\n const value = d3.create('div').node();\n function update() {\n d3.select(value).text(scale(chaos.value));\n board.value = randomBoard(width, height, scale(chaos.value));\n }\n update();\n d3.select(chaos).on('input', update);\n return html`

${chaos}${value}${board}

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