➖ 生成广义康托尔集Generate Generalized Cantor Set

使用说明与常见问题How-to & FAQ

「生成广义康托尔集」是什么？What is the Generate Generalized Cantor Set tool?

生成广义康托尔梳：每步按可调保留比例去掉中间空隙（左右对称）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a generalized Cantor comb with an adjustable keep ratio (symmetric). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.

如何使用「生成广义康托尔集」？How do I use the Generate Generalized Cantor Set tool?

在「生成广义康托尔集」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 Generalized Cantor Set: Set "Width", "Height", "Padding", "Line width", "Iterations", then click "Draw", "Download PNG".

和经典康托尔集有何不同？How does this differ from the classic Cantor set?

经典康托尔集每一步在左右各保留 1/3、去掉中间 1/3；这里可以把每侧保留比例设成 0.05–0.45 之间的任意值，左右对称，中间去掉 1−2k。比例越小，空隙越宽、线段消失得越快。The classic Cantor set keeps 1/3 on each side and removes the middle third; here the keep ratio k per side can be anything from 0.05 to 0.45, symmetric on both sides, removing 1−2k from the middle. Smaller ratios give wider gaps and segments that vanish faster.

保留 1/3 时？When keep = 1/3?

输入 0.3333 左右就与经典三等分康托尔梳一致。比例必须在 0.05–0.45 之间；超出范围或留空时会提示，不会悄悄改成边界值。Around 0.3333 it matches the classic middle-third comb. The ratio must be 0.05–0.45; out-of-range or empty values give a message instead of being moved to the limit silently.

有哪些选项可以调整？What options can I adjust?

「生成广义康托尔集」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 1–9；「每侧保留比例」默认 0.3，范围 0.05–0.45；「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 Generalized 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 1–9; "Keep ratio per side" default 0.3, range 0.05–0.45; "Background" default #ffffff; "Line" default #1e3a8a. The result always uses the current settings.

「生成广义康托尔集」免费吗？需要注册吗？Is the Generate Generalized Cantor Set free? Do I need an account?

「生成广义康托尔集」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 Generalized 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.