擴散戰線：原子之境DIFFUSION RIFT · REALM OF ATOMS
擴散戰線：原子之境・遊戲說明書Diffusion Rift: Realm of Atoms · Game Manual
工程材料 CT3309301 第五章「擴散」的教學 MOBA 遊戲。你和隊友（真人或電腦）組成 5 人的「晶格同盟」，對抗電腦控制的「熔爐軍團」。摧毀對方主堡即獲勝。整張地圖的地面都在即時解菲克第二定律——擴散不只是課本上的公式，而是戰場的規則。A teaching MOBA for Ch.05 Diffusion of CT3309301 Engineering Materials. You and your teammates (human or CPU) form the 5-hero Crystal Concord against the CPU Furnace Legion. Destroy the enemy core to win. The ground of the whole map solves Fick's second law in real time: diffusion isn't just a formula here, it is the rule of the battlefield.
1. 快速開始1. Quick start
- 按「開始遊戲」，欣賞約 48 秒的片頭動畫（可略過）。Press Start Game and enjoy the ~48 s opening film (skippable).
- 選擇英雄、人數與難度，按「出征」。Pick a hero, the number of players and a difficulty, then press Deploy.
- 跟著我方「原子兵」沿路推進，擊敗敵兵賺金與經驗；等級 4 答對研究題解鎖大招。Push with your atomling waves, last-hit enemies for gold and XP, and at level 4 answer a research question to unlock your ultimate.
- 回到主堡附近打開「實驗室」購買裝備，或隨時答題換取研究補助金。Open the Lab near your base to buy items, or answer questions anytime for research gold.
2. 操作方式2. Controls
| 動作Action | 電腦Keyboard & mouse | 手機／平板Phone / tablet | 手把Gamepad |
|---|---|---|---|
| 移動Move | W A S D / ←↑→↓ 或右鍵點地面or right-click ground | 螢幕搖桿（設定開啟），或點地面On-screen stick (enable in Settings) or tap the ground | 左類比Left stick |
| 普攻Attack | 按住 空白鍵；左鍵點敵人鎖定Hold Space; left-click an enemy to focus it | 按住「攻擊」；點敵人鎖定Hold ATK; tap an enemy to focus it | A |
| 技能 1／2／大招Skill 1 / 2 / Ult | Q／E／R（朝滑鼠方向施放）Q / E / R (aimed at the mouse) | 點一下自動瞄準；拖曳技能鈕可手動瞄準Tap to auto-aim; drag the button to aim | X / Y / RB |
| 回城Recall | B | 「回城」鈕（4 秒，受傷會中斷）Recall button (4 s, broken by damage) | B |
| 濃度探針Concentration probe | V（朝滑鼠方向）V (toward the mouse) | 「探針」鈕（朝面向）Probe button (facing direction) | – |
| 實驗室／商店Lab / shop | L | 「實驗室」鈕Lab button | LB |
| 戰況表Scoreboard | 按住 TabHold Tab | ☰ | Back |
| 暫停／全螢幕Pause / full screen | P, Esc / F | ❚❚ / ⛶ | Start |
按鍵可在「設定 → 自訂按鍵」修改。「鎖英雄」鈕可讓普攻優先打敵方英雄。手機請橫放並按「全螢幕」；全螢幕時畫面固定，不會被拖動或縮放。Rebind keys under Settings → Key bindings. The Heroes button makes attacks prefer enemy heroes. On phones, turn sideways and press Fullscreen; the view is then locked against dragging and zooming.
3. 地圖：三條路徑與濃度場3. The map: three paths and the concentration field
地圖 6000 × 6000，左下是我方晶都，右上是敵方熔爐要塞。三條路的地面圖案直接畫出擴散機制：The 6000 × 6000 map has your citadel at lower left and the Furnace fortress at upper right. Each path's floor shows its mechanism:
- 晶界捷徑（上路）Grain-boundary path (top)多晶晶粒與發光晶界，D 最大（×4）。Polycrystal grains with glowing boundaries; largest D (×4).
- 空位之路（中路）Vacancy path (mid)規則原子排列中散布紫色空位，D ×1.6。A regular lattice dotted with violet vacancies; D ×1.6.
- 間隙之路（下路）Interstitial path (bottom)大原子之間的綠色小原子在間隙中，D ×2.6。Small green atoms in the gaps between large atoms; D ×2.6.
- 等溫河與野區Isotherm river & jungle河道 D 很小，像擴散屏障；野區 D 較小。The river has a tiny D and acts as a barrier; the jungle has a smaller D.
地面的藍色／紅色就是溶質濃度 C(x,y,t)。每座防禦塔與主堡都是固定表面濃度 Cs 的「源」，原子兵走過會留下溶質，技能也能注入溶質或升溫。細線是等濃度線（每 10%），亮白線是擴散前緣（C = 50%），橘色光暈是升溫區。濃度場由 Fick 第二定律在背景執行緒（Web Worker）即時計算；選「硬體加速」時還會用 WebGPU 運算。The blue/red tint is the solute concentration C(x,y,t). Every tower and core is a source held at a fixed surface concentration Cs; atomlings deposit solute as they march, and skills inject solute or heat. Thin lines are iso-concentration contours (every 10%), the bright line is the diffusion front (C = 50%) and orange glow marks heated ground. Fick’s second law is solved live in a background thread (Web Worker), on WebGPU compute when Hardware is selected.
| 遊戲規則Game rule | 對應觀念Concept |
|---|---|
| 站在我方溶質中（C′ > 0.3）移速 +10% 並回血；在敵方溶質中移速 −10%In your own solute (C′ > 0.3): +10% speed and regen; in enemy solute: −10% speed | 濃度場、由高往低擴散Concentration field; flow from high to low |
| 防禦塔若被敵方溶質包圍，受到傷害 +20%Towers surrounded by enemy solute take +20% damage | 滲透與累積（非穩態）Penetration and accumulation (non-steady state) |
| 摧毀防禦塔＝移除一個源，領地會逐漸退縮Destroying a tower removes a source, so territory recedes | 邊界條件改變後的非穩態擴散Non-steady diffusion after a boundary change |
| 升溫處擴散變快Diffusion speeds up where it's hot | D = D₀ exp(−Qd/RT) |
| HUD 顯示所在位置的 C′、D 與 TThe HUD shows C′, D and T where you stand | 讀數練習Reading the variables |
4. 英雄4. Heroes
| 英雄Hero | 定位Role | 技能與觀念Skills & concept |
|---|---|---|
| 菲克・梯度賢者Fick, the Gradient Sage | 法師Mage | 梯度衝擊（傷害隨 |∇C| 增加）、通量領域、穩態光束——菲克第一定律與穩態擴散Gradient Bolt (damage grows with |∇C|), Flux Field, Steady-State Beam: Fick's first law and steady state |
| 布朗・隨機漫步者Brown, the Random Walker | 刺客Assassin | 隨機漫步（三段隨機跳躍，位移 ≈ √3 步長）、熱振動、布朗風暴——擴散的微觀本質Random Walk (three random hops, displacement ≈ √3 steps), Thermal Jitter, Brownian Storm: the microscopic picture |
| 阿瑞尼斯・熔爐守護者Arrhenius, Keeper of the Furnace | 輔助Support | 活化火焰、升溫領域、熔爐之陽——溫度與活化能Activation Flame, Heat Zone, Furnace Sun: temperature and activation energy |
| 小碳・間隙遊俠Carbon, the Interstitial Ranger | 射手Marksman | 間隙穿梭、滲碳箭、表面硬化——間隙擴散與滲碳Interstitial Dash, Carburize Arrow, Case Hardening: interstitial diffusion and carburizing |
| 空位騎士・虛空守衛Vacancy, the Hollow Guardian | 坦克Tank | 位置交換（與目標互換位置）、空位之盾、晶格崩塌——空位機制Site Swap (trade places with the target), Vacancy Shield, Lattice Collapse: the vacancy mechanism |
| 時之主・時間平方根之主Chronos, Lord of √t | 控制Controller | 誤差函數波（傷害 ∝ 1−erf）、時間膨脹、√t 擴張（r = k√t）——非穩態擴散與 x ∝ √(Dt)Erf Wave (damage ∝ 1−erf), Time Dilation, √t Expansion (r = k√t): non-steady diffusion and x ∝ √(Dt) |
開啟「劇情提示」時，你每次施放技能，畫面下方會顯示該技能對應的擴散觀念。With Story hints on, every skill you cast shows its diffusion concept at the bottom of the screen.
5. 實驗室、研究與裝備5. Lab, research and items
- 研究補助：在實驗室答題，答對 +130 金；答錯需冷卻 15 秒。題庫 40 題，涵蓋課本 5.1–5.5 節與例題 5.1–5.4。Research grant: answer in the Lab for +130 gold; a wrong answer adds a 15 s cooldown. 40 questions cover Sections 5.1–5.5 and Examples 5.1–5.4.
- 大招研究：英雄升到 4 級時，答對一題即解鎖大招（答錯 12 秒後可再試）。Ultimate research: at level 4, answer one question correctly to unlock your ultimate (retry 12 s after a miss).
- 裝備只能在主堡附近或陣亡時購買，最多 6 件；可半價（60%）賣回。Items can be bought only near your base or while dead, up to 6, and sold back for 60%.
- 單機模式下，開啟實驗室或答題時遊戲會暫停。In solo play the game pauses while the Lab or a question is open.
6. 野區與史詩怪6. Jungle and epic monsters
- 藍色元素：「通量」增益，冷卻加速 20%（90 秒）。紅色元素：「熾熱」增益，普攻灼燒（90 秒）。Blue elemental: Flux buff, 20% faster cooldowns (90 s). Red elemental: Heat buff, burning attacks (90 s).
- 活化能巨龍（上河道）：全隊 +12% 傷害並持續散布我方溶質 120 秒。Activation Dragon (upper river): team +12% damage and solute aura for 120 s.
- 平衡魔像（下河道）：全隊金錢經驗，接下來 150 秒兵線強化。Equilibrium Golem (lower river): team gold and XP, plus stronger waves for 150 s.
7. 勝利、計分與排行榜7. Victory, scoring and the leaderboard
外塔未破時內塔無敵；任一路內塔被破，主堡才會受傷。分數 = 勝負 + 擊殺／助攻 − 陣亡 + 補兵 + 傷害 + 推塔 + 答對題數 × 90 + 勝利時間獎勵，再乘上難度係數（簡單 0.7、普通 1、困難 1.35）。戰後「實驗報告」要你用 1 − erf(x/L) 擬合中路的濃度剖面，R² 越高最多再加 300 分。排行榜只顯示暱稱，請勿使用真實姓名或學號。Inner towers are immune while their outer tower stands; the core takes damage only after an inner tower falls. Score = result + kills/assists − deaths + last hits + damage + towers + correct answers × 90 + a speed bonus on victory, times the difficulty factor (Easy 0.7, Normal 1, Hard 1.35). The post-match Lab Report asks you to fit the mid-path profile with 1 − erf(x/L) for up to 300 bonus points. The leaderboard shows nicknames only; don't use your real name or student ID.
8. 多人連線（1–5 人）8. Online play (1–5 players)
- 房主：出征準備 → 選擇人數 2–5（自動切到「開房」）→ 出現 6 碼房號、連結與 QR code。Host: in Muster pick 2–5 players (switches to Host) and a 6-character room code, link and QR code appear.
- 同學：開同一篇文章 → 開始遊戲 → 加入 → 輸入房號（或掃 QR、開連結自動加入），選好英雄與暱稱。Classmates: open the same post → Start Game → Join → enter the code (or scan the QR / open the link), then pick a hero and nickname.
- 人齊後房主按「出征」。所有人同在藍隊合作對抗電腦。房主的電腦負責運算，請房主使用較穩定的網路與裝置。When everyone is in, the host presses Deploy. Everyone plays together on the blue team against the CPU. The host's device runs the simulation, so the host should use a stable device and network.
- 有人斷線時由電腦暫代，重新整理同一分頁可回到原座位。If someone drops, the CPU takes over; reloading the same tab returns them to their seat.
9. 設定與存檔9. Settings and saves
- 語言：中文／中文 English／English。背景音樂（預設關閉）依場景切換：標題、選角、片頭、對線、中期、團戰、實驗室、勝利、失敗、排行榜共 10 首原創樂曲，每首有 9–10 個立體聲左右分佈的樂器音軌加 1 個獨立鼓組音軌，以 General MIDI 音色庫即時演奏（瀏覽器不支援時自動改用合成器版本）。音效預設開啟，三種音量可分別調整。Language: Chinese / bilingual / English. Music (off by default) follows the scene with 10 original pieces (title, muster, opening, lane, mid game, team fight, Lab, victory, defeat, leaderboard); each has 9–10 instrument tracks panned across the stereo field plus 1 independent drum track, played live through a General MIDI sound bank (a synthesized fallback is used if the browser cannot). Sound effects are on by default; three volume sliders.
- 繪圖：硬體加速（預設，Phaser 3 WebGL 繪圖 + WebGPU 擴散運算）或軟體（Canvas 2D + CPU）；裝置不支援時自動改用軟體。畫質：流暢 720p（預設，地圖貼圖較小、適合手機）／標準 1080p／高 2K（1440p）。Renderer: Hardware (default: Phaser 3 WebGL drawing + WebGPU diffusion compute) or Software (Canvas 2D + CPU); it falls back automatically. Quality: Smooth 720p (default, lighter map textures for phones) / Standard 1080p / High 2K (1440p).
- 螢幕搖桿（預設關閉）、劇情提示（預設開啟）、濃度場顯示、自訂按鍵、全螢幕（預設關閉）、暫停、重新開始。On-screen stick (off by default), story hints (on), field overlay, key bindings, full screen (off), pause and restart.
- 存檔：3 個存檔欄 + 每 30 秒自動存檔，可匯出／匯入 .json。連線對戰無法存檔。Saves: 3 slots plus a 30-second auto-save, with .json export/import. Online matches can't be saved.
© 2026 AEML, NTUST（國立臺灣科技大學 先進工程材料實驗室）。課本：Callister & Rethwisch, Materials Science and Engineering, 8e, Ch.5。插圖為原創 AI 生成作品。© 2026 AEML, NTUST. Textbook: Callister & Rethwisch, Materials Science and Engineering, 8e, Ch.5. Illustrations are original AI-generated artwork.
10. 新功能：教學、課堂快速戰、探針、計算題、戰爭迷霧10. New: tutorial, class quick match, probe, calculation problems, fog of war
- 新手教學（3 分鐘）Tutorial (3 min)標題畫面按「新手教學」。依序完成：移動 → 普攻訓練史萊姆 → 放技能 → 讀濃度場並使用探針 → 在實驗室答一題 → 回城。Press Tutorial on the title screen and complete: move → attack the training slime → cast a skill → read the field and use the probe → answer one Lab question → recall.
- 課堂快速戰（6–8 分鐘）Class quick match (6–8 min)只有中路、沒有野區，所有英雄從 3 級、1400 金開始，兵線每 20 秒一波，重生較快。8:00 時若主堡都未被破，由剩餘塔與主堡血量較多的一方獲勝。出征畫面也可切換「完整三路 5v5」或「課堂快速」。Mid lane only, no jungle; every hero starts at level 3 with 1400 gold, waves every 20 s and faster respawns. At 8:00, if neither core has fallen, the side with more structure health wins. You can also switch Battlefield on the muster screen.
- 濃度探針Concentration probe所有英雄都有：按 V 或「探針」鈕，沿一條 1600 單位的線即時顯示 C(x) 剖面（藍＝我方溶質、紅＝敵方），並標出最陡處（|dC/dx| 最大 ⇒ 通量 J 最大）。持續 9 秒、冷卻 4 秒。Every hero has it: press V or Probe to plot the live C(x) profile along a 1600-unit line (blue = our solute, red = theirs), with the steepest point marked (largest |dC/dx| ⇒ largest flux J). Lasts 9 s, 4 s cooldown.
- 計算挑戰Calculation challenge實驗室裡的「挑戰計算題」會隨機出例題 5.1（穩態通量）、5.2（滲碳時間，需查 erf 表）、5.3（Dt = 常數）、5.4（查表 5.2 求 D）的變化題。以「數值 × 10 的次方」輸入，誤差 ±3% 內即正確，+200 金，並附詳解。In the Lab, Solve a problem gives randomized versions of Ex. 5.1 (steady-state flux), 5.2 (carburizing time, erf table), 5.3 (Dt = constant) and 5.4 (D from Table 5.2). Enter mantissa × power of ten; within ±3% is correct for +200 gold, with a worked solution.
- 戰爭迷霧與草叢Fog of war and bushes只看得到我方英雄、小兵、塔與主堡視野內的敵人。站進草叢的英雄會隱身（我方看到半透明），除非敵人走進同一草叢、靠近 280 單位內，或你剛攻擊／施法（1 秒內會現形）。電腦對手與小兵也遵守這個規則。You only see enemies inside the vision of your heroes, minions, towers and core. A hero standing in a bush is hidden (shown translucent to allies) unless an enemy enters the same bush, comes within 280 units, or the hero has just attacked or cast (revealed for 1 s). AI heroes and minions obey the same rule.
- 美術Art地圖由 OpenArt 生成的材質與道具離線烘焙成 36 張精細貼圖；英雄、小兵、防禦塔、主堡與野怪皆為 OpenArt 角色圖，並加上走路擺動、攻擊衝刺、施法光暈與受擊閃光等動態。The map is baked offline into 36 detailed tiles from OpenArt textures and props; heroes, minions, towers, cores and monsters are OpenArt sprites animated with walk bob, attack lunge, cast glow and hit flash.