{"id":"lesson-02","number":2,"title":"數學之美：向量與粒子","tool":"p5.js","date":"2026-10-06","time":"19:00–21:30","hasNotes":true,"notes":{"title":"數學之美：向量與粒子","status":"課後版 v2（2026-10-08 依逐字稿重寫）","date":"2026-10-06","toc":[{"id":"s-1","text":"這堂在做什麼","level":2},{"id":"s-2","text":"開場：先講概念，再進程式","level":2},{"id":"s-3","text":"近況：讓作品可以被演奏","level":2},{"id":"s-3-1","text":"Open Audio Visual","level":3},{"id":"s-3-2","text":"入門 MIDI 控制器","level":3},{"id":"s-3-3","text":"實驗室：用講話寫作品","level":3},{"id":"s-4","text":"作業賞析：玩到想把它留下來","level":2},{"id":"s-5","text":"粒子藝術：一大群會跑來跑去的東西","level":2},{"id":"s-5-1","text":"三個通則","level":3},{"id":"s-5-2","text":"粒子也可以是筆刷","level":3},{"id":"s-5-3","text":"Circle Packing","level":3},{"id":"s-6","text":"粒子案例：從花到神經系統","level":2},{"id":"s-6-1","text":"哲宇的作品","level":3},{"id":"s-6-2","text":"國際案例","level":3},{"id":"s-7","text":"向量：把一組數字包成一支箭頭","level":2},{"id":"s-8","text":"加速度、空氣阻力與反彈","level":2},{"id":"s-9","text":"力：誰比較容易被推動","level":2},{"id":"s-9-1","text":"吸引與排斥","level":3},{"id":"s-9-2","text":"宇宙：粒子彼此拉扯","level":3},{"id":"s-10","text":"力場與 Perlin noise","level":2},{"id":"s-10-1","text":"給空間裡每個位置一個方向","level":3},{"id":"s-10-2","text":"Perlin noise：一坨連續的亂數","level":3},{"id":"s-10-3","text":"把軌跡留下來","level":3},{"id":"s-11","text":"粒子的誕生與死亡","level":2},{"id":"s-12","text":"Demo 1：一顆會彈的球","level":2},{"id":"s-13","text":"Demo 2：粒子槍","level":2},{"id":"s-14","text":"Demo 3：Noise Field","level":2},{"id":"s-15","text":"收尾：回顧，再多玩幾招","level":2},{"id":"s-15-1","text":"回顧","level":3},{"id":"s-15-2","text":"幾個可以直接加進作業的玩法","level":3},{"id":"s-16","text":"課堂問答","level":2},{"id":"s-16-1","text":"近況與器材","level":3},{"id":"s-16-2","text":"概念與運算","level":3},{"id":"s-16-3","text":"寫程式","level":3},{"id":"s-16-4","text":"上課與提問","level":3},{"id":"s-17","text":"作業與下一堂","level":2},{"id":"s-17-1","text":"作品二：Flow Field","level":3},{"id":"s-17-2","text":"下一堂：自然的演算法","level":3},{"id":"s-18","text":"卡住的時候","level":2},{"id":"s-19","text":"延伸資源","level":2}],"segments":[{"html":"
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2026-10-06（二）19:00～21:16 線上直播（錄影 2:16:34）

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這堂在做什麼

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前兩堂常常講到一半就突然跳進程式，這堂換了一個走法：先把概念講清楚，看完參考作品，再踏進程式。所以前一個小時幾乎沒有寫程式，從粒子藝術的作品看起，看大家怎麼用一大群會動的小東西畫出河流、花和風，再用互動模組把向量、速度、加速度、力場和 Perlin noise 一個一個拆開。後一個小時連寫三個 Demo，一個長成下一個：先是一顆會彈的球，再把球包成工廠、按著滑鼠噴出一整串彩色粒子，最後讓粒子撒滿畫面，順著 noise 排出來的地形流成河。

\n"},{"locked":true,"id":"s-2","title":"開場：先講概念，再進程式"},{"locked":true,"id":"s-3","title":"近況：讓作品可以被演奏"},{"locked":true,"id":"s-4","title":"作業賞析：玩到想把它留下來"},{"locked":true,"id":"s-5","title":"粒子藝術：一大群會跑來跑去的東西"},{"locked":true,"id":"s-6","title":"粒子案例：從花到神經系統"},{"locked":true,"id":"s-7","title":"向量：把一組數字包成一支箭頭"},{"locked":true,"id":"s-8","title":"加速度、空氣阻力與反彈"},{"locked":true,"id":"s-9","title":"力：誰比較容易被推動"},{"locked":true,"id":"s-10","title":"力場與 Perlin noise"},{"locked":true,"id":"s-11","title":"粒子的誕生與死亡"},{"locked":true,"id":"s-12","title":"Demo 1：一顆會彈的球"},{"locked":true,"id":"s-13","title":"Demo 2：粒子槍"},{"locked":true,"id":"s-14","title":"Demo 3：Noise 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與實驗室"},{"t":"13:53","sec":833,"title":"實驗室與 AI 共創","note":"介紹作品族譜、實驗室系統與《宇宙熵時》，談用對話、決策、MIDI 錄製與 AI 迭代作品。","part":"近況：Open Audio Visual 與實驗室"},{"t":"21:22","sec":1282,"title":"第一堂作業賞析","note":"看動態幾何、格子、花瓣、稻田、碎片與下雨等作品，談材質、景深、AI 協作與粒子物件。","part":"作業賞析"},{"t":"30:00","sec":1800,"title":"粒子藝術的基本結構","note":"把粒子說成可動、可大量重複、受物理法則影響的物件，從 Blue Particle Rain 進入力場與軌跡。","part":"主要課程：粒子、向量與力場"},{"t":"32:23","sec":1943,"title":"粒子作為畫筆與 Circle Packing","note":"說明粒子不一定是圓形，也可以是方形、紙片或筆刷，並介紹不重疊排列的 Circle Packing。","part":"主要課程：粒子、向量與力場"},{"t":"36:21","sec":2181,"title":"粒子作品案例：從花到神經系統","note":"以《咖啡幻夢》、《彼岸花》、Golden Evolution、Electriz、《混亂舞者》 與 Nervous System 說明粒子演化。","part":"主要課程：粒子、向量與力場"},{"t":"41:30","sec":2490,"title":"國際案例：風場與資料藝術","note":"看 Wind Map、Wind of Boston、Fidenza、Perlin Noise Flow Field 與 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和摩擦。","part":"Demo 1：一顆會彈的球"},{"t":"1:24:27","sec":5067,"title":"學員 Ball 程式除錯","note":"處理球彈不起來與飛出去的程式，修正 Vy 反向寫法以及位置沒有加上速度的問題。","part":"Demo 1：一顆會彈的球"},{"t":"1:25:44","sec":5144,"title":"Particle Gun 的結構","note":"介紹 Class、constructor、this、Particle 的位置速度加速度，以及每顆粒子的 update 和 draw。","part":"Demo 2：Particle Gun"},{"t":"1:33:23","sec":5603,"title":"陣列與 forEach","note":"用 particles 陣列和 forEach 管理多顆粒子，控制滑鼠按下才生成，並逐顆更新與繪製。","part":"Demo 2：Particle Gun"},{"t":"1:38:44","sec":5924,"title":"生命與清理","note":"處理粒子太多的問題，加上半徑、顏色、life 倒數與 filter，只留下 life 大於零的粒子。","part":"Demo 2：Particle Gun"},{"t":"1:46:39","sec":6399,"title":"兩張 noise 切片推動粒子","note":"從 Particle Gun Fork 出格點粒子，用 Noise 的不同切片給加速度、map 到負一至一，再用摩擦做出流動力場。","part":"Demo 3：Noise Field"},{"t":"1:54:30","sec":6870,"title":"回顧、像素取值與作業","note":"回顧向量、力場、Noise 和生命週期，示範用 get() 取影像像素，說明三個 Demo 的練習與參數延伸。","part":"回顧與作業"},{"t":"2:10:27","sec":7827,"title":"收尾問答與下週預告","note":"回答 Pinterest、MIDI、私訊和演算法課程問題，預告自然演算法與 flocking，最後請大家填問卷。","part":"回顧與作業"}],"summary":"2 小時 16 分。先回答 Discord 的問題、分享 Open Audio Visual 改版與實驗室系統，接著看第一堂的作業；主要課程從粒子藝術的作品案例講到向量、加速度、力場與 noise 的取值，再用三個 Demo 依序做出會彈的球、按住滑鼠噴出粒子的粒子槍，以及用 noise 兩張切片推動的粒子力場。作業是「作品二：Flow Field」，10/12（一）21:00 前交 Hahow。","duration":"2:16:34","plan":{"topic":"向量、力場、粒子系統","output":"Flow Field 作品","stage":"友善入門","difficulty":3},"sections":19,"qaCount":23,"homework":{"title":"作品二　Flow Field","steps":["把課堂上的三個 Demo（Ball、Particle Gun、Particle Field）各練過一遍","每個 Demo 都改參數，調到自己喜歡、覺得好玩的狀態","參考本單元的粒子 moodboard 或自己的 moodboard，往想要的藝術感覺調","替作品命名、寫描述，從日常取材（每天的雨、飄過的灰塵…）","進階：載入一張圖，用 get() 取像素顏色當粒子參數","交到 Hahow 作業區「作品二」，10/12（一）21:00 前；Discord #作業分享 貼一份"],"source":"[2:01:23]、[2:08:03]～[2:09:54]；題目與截止照講綱（課堂上只在 /live 畫面出現）"},"quotes":[{"t":"1:55","text":"「我們先把概念講清楚，然後看參考的作品，看完參考的作品之後，我們再踏到程式裡面，不會讓大家猝不及防的就被程式攻擊這樣」"},{"t":"16:47","text":"「那什麼東西是在 AI 時代沒有辦法馬上被做完的東西？」"},{"t":"17:03","text":"「我的想法跟審美才是作品的本身這樣」"}],"quotesTotal":8,"resources":[{"group":"範例程式（OpenProcessing）","items":[{"title":"w2-1 Ball","url":"https://openprocessing.org/@cheyuwu/3027925","note":"Demo 1：位置、速度、加速度、反彈"},{"title":"w2-2 Particle Gun","url":"https://openprocessing.org/@cheyuwu/3027928","note":"Demo 2：class、陣列、按住滑鼠噴粒子"},{"title":"w2-3 Particle Field","url":"https://openprocessing.org/@cheyuwu/3027936","note":"Demo 3：noise 兩張切片推動的粒子力場"},{"title":"課堂現場版：Particle Gun","url":"https://openprocessing.org/@cheyuwu/3028033"}]},{"group":"哲宇的案例","items":[{"title":"咖啡幻夢","url":"https://cheyuwu.com/zh/work/coffee-dreamscape/"},{"title":"彼岸花","url":"https://cheyuwu.com/zh/work/flower-of-the-other-shore/"},{"title":"LG 永恆花境","url":"https://cheyuwu.com/zh/exhibitions/lg-eternal-floral-realm/"},{"title":"220913 Golden Evolution","url":"https://cheyuwu.com/zh/sketch/1645015/"},{"title":"Electriz","url":"https://cheyuwu.com/zh/work/electriz/"},{"title":"混亂舞者 Chaos 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19:00–19:03　直播與聊天室確認

19:03–19:08　回答大家的問題

19:08–19:15　近況更新

19:15–19:25　作業賞析

19:25–20:00　主要課程：向量、粒子、力場

20:00–20:15　Demo 1：Ball 一顆球

20:15–20:30　Demo 2：Particle Gun 粒子槍

20:30–20:45　Demo 3：Particle Field 粒子力場

20:45–21:00　課後問答與作業說明

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