➖ 生成 Smith–Volterra–Cantor 集Generate Smith–Volterra–Cantor Set
生成 Smith–Volterra–Cantor（肥康托尔）集梳状图：第 n 步从每段中间去掉长 1/4ⁿ（即 1/2²ⁿ）的空隙。第一行是原线段，第 k+1 行是做完 k 步后的结果。导出 PNG。Generate a Smith–Volterra–Cantor (fat Cantor) set as a comb: at step n remove a middle gap of length 1/4ⁿ (that is 1/2²ⁿ) from each interval. The first row is the original segment and row k+1 shows the result after k steps. Export PNG.
使用说明与常见问题How-to & FAQ
「生成 Smith–Volterra–Cantor 集」是什么？What is the Generate Smith–Volterra–Cantor Set tool?
生成 Smith–Volterra–Cantor（肥康托尔）集梳状图：第 n 步从每段中间去掉长 1/4ⁿ（即 1/2²ⁿ）的空隙。第一行是原线段，第 k+1 行是做完 k 步后的结果。导出 PNG。Generate a Smith–Volterra–Cantor (fat Cantor) set as a comb: at step n remove a middle gap of length 1/4ⁿ (that is 1/2²ⁿ) from each interval. The first row is the original segment and row k+1 shows the result after k steps. Export PNG.
如何使用「生成 Smith–Volterra–Cantor 集」？How do I use the Generate Smith–Volterra–Cantor Set tool?
在「生成 Smith–Volterra–Cantor 集」中，按需设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」等选项，然后点击「绘制」、「下载 PNG」按钮即可。In the Generate Smith–Volterra–Cantor Set: Set "Width", "Height", "Padding", "Line width", "Iterations", then click "Draw", "Download PNG".
肥康托尔是什么意思？What does "fat Cantor" mean?
第 n 步从剩下的 2ⁿ⁻¹ 段中间各去掉长 1/4ⁿ 的一小段，所以去掉的总长只有 1/4 + 2/16 + 4/64 + … = 1/2，剩下的集合仍有长度 1/2（正测度），却不包含任何区间。做完 k 步后剩余长度是 1/2 + (1/2)^(k+1)。「迭代次数」n 画出 n+1 行：原线段和第 1…n 步。Step n removes a piece of length 1/4ⁿ from the middle of each of the 2ⁿ⁻¹ remaining intervals, so the total removed is only 1/4 + 2/16 + 4/64 + … = 1/2. The set left over still has length 1/2 (positive measure) yet contains no interval. After k steps the remaining length is 1/2 + (1/2)^(k+1). Iterations n draws n+1 rows: the original segment and steps 1…n.
颜色和细节？Colours and detail?
线段用「线条」颜色填实，所以没有单独的「填充」设置；第 5 步之后空隙已小于 1 像素，页面会提示细节已小于像素。Bars are filled in the Line colour, so there is no separate Fill setting; after step 5 the gaps are thinner than a pixel and the page notes that the detail is finer than a pixel.
和经典康托尔？Vs classic?
经典每步去 1/3；SVC 去的更短，故「肥」。Classic removes 1/3 each time; SVC removes less, so it is fat.
有哪些选项可以调整？What options can I adjust?
「生成 Smith–Volterra–Cantor 集」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；「迭代次数」默认 5，范围 1–8；「背景」默认 #ffffff；「线条」默认 #1e3a8a。每次生成结果都按当前设置处理。Settings in the Generate Smith–Volterra–Cantor Set — "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; "Iterations" default 5, range 1–8; "Background" default #ffffff; "Line" default #1e3a8a. The result always uses the current settings.
「生成 Smith–Volterra–Cantor 集」免费吗？需要注册吗？Is the Generate Smith–Volterra–Cantor Set free? Do I need an account?
「生成 Smith–Volterra–Cantor 集」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 Generate Smith–Volterra–Cantor Set is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.