⬚ 康托尔尘分形Draw a Cantor Dust Fractal
绘制二维康托尔尘：把正方形反复分成 9 格，只保留四角（或四角+中心）。可选常规尘、连通尘、箱分形，可调迭代、缩小比、颜色，导出 PNG。Draw 2-D Cantor dust: repeatedly split a square into nine and keep the four corners (or corners plus centre). Choose regular, connected or box dust, set iterations and reduction, colours, export PNG.
使用说明与常见问题How-to & FAQ
「康托尔尘分形」是什么？What is the Draw a Cantor Dust Fractal tool?
绘制二维康托尔尘：把正方形反复分成 9 格，只保留四角（或四角+中心）。可选常规尘、连通尘、箱分形，可调迭代、缩小比、颜色，导出 PNG。Draw 2-D Cantor dust: repeatedly split a square into nine and keep the four corners (or corners plus centre). Choose regular, connected or box dust, set iterations and reduction, colours, export PNG.
如何使用「康托尔尘分形」？How do I use the Draw a Cantor Dust Fractal tool?
在「康托尔尘分形」中，按需设置「宽度」、「高度」、「边距」、「线宽」、「类型」等选项，然后点击「绘制」、「下载 PNG」按钮即可。Set the canvas "Width" and "Height", the "Padding" around the drawing and the "Line width", choose the dust "Type", the number of "Iterations" and the "Reduction" factor, pick the "Background", "Line" and "Fill" colours, then click "Draw". "Download PNG" saves the picture at the canvas size.
三种类型有什么区别？How do the three types differ?
常规尘只留四角，是康托尔集的笛卡尔积；连通尘额外保留中心块；箱分形（Dusty Dust）对中心继续细分，每步大约 ×5 块。Regular dust keeps only the four corners (Cantor set × Cantor set). Connected dust also keeps the centre block. The box fractal further subdivides the centre (~×5 blocks per step).
缩小比是什么？What is Reduction?
缩小比 r 表示每一步把正方形分成 r×r 格、只保留四角（连通尘和箱分形另外保留正中一块）。默认 3 是经典的三等分；可选 3–5，r 越大保留的块越小、空隙越大。2 不可用：2×2 时四个角就是全部格子，不会留下空隙。Reduction r splits the square into r×r cells each step and keeps the four corners (connected and box dust also keep one centred block). 3 is the classic middle-thirds split; 3–5 are allowed, and a larger r keeps smaller blocks with wider gaps. 2 is not allowed: in a 2×2 grid the four corners are every cell, so no gaps would remain.
有哪些选项可以调整？What options can I adjust?
「康托尔尘分形」的设置：「宽度」默认 512，范围 64–2048；「高度」默认 512，范围 64–2048；「边距」默认 20，范围 0–256；「线宽」默认 2，范围 0.5–40；「类型」可选 常规尘（四角）、连通尘（四角+中心）、箱分形（中心再细分）（默认 常规尘（四角））；「迭代次数」默认 4，范围 1–6；「缩小比」默认 3，范围 3–5；「背景」默认 #ffffff；「线条」默认 #1e3a8a；「填充」默认 #93c5fd。改动任一选项后结果会按新设置重新生成。Settings in the Draw a Cantor Dust Fractal — "Width" default 512, range 64–2048; "Height" default 512, range 64–2048; "Padding" default 20, range 0–256; "Line width" default 2, range 0.5–40; "Type": Regular (4 corners), Connected (+centre), Box fractal (default Regular (4 corners)); "Iterations" default 4, range 1–6; "Reduction" default 3, range 3–5; "Background" default #ffffff; "Line" default #1e3a8a; "Fill" default #93c5fd. Changing any option regenerates the result with the new setting.
「康托尔尘分形」免费吗？需要注册吗？Is the Draw a Cantor Dust Fractal free? Do I need an account?
「康托尔尘分形」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Draw a Cantor Dust Fractal is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.