▣ 生成谢尔宾斯基方块Generate Sierpinski Square
「谢尔宾斯基方块」没有独立的标准定义。本页的规则是：把正方形分成 3×3 九格，只保留四个角，再对每个角重复——这正是康托尔尘（Cantor dust），结果与「生成康托尔尘」相同，完整说明见该工具。去掉中间一格、保留 8 格的版本是谢尔宾斯基地毯。导出 PNG。There is no separate standard definition of a "Sierpinski square". The rule used here, split a square into a 3×3 grid, keep only the four corners and repeat on each, is exactly Cantor dust, the same result as Generate Cantor Dust, which has the full explanation. The version that removes only the centre cell and keeps 8 is the Sierpinski carpet. Export PNG.
使用说明与常见问题How-to & FAQ
「生成谢尔宾斯基方块」是什么？What is the Generate Sierpinski Square tool?
「谢尔宾斯基方块」没有独立的标准定义。本页的规则是：把正方形分成 3×3 九格，只保留四个角，再对每个角重复——这正是康托尔尘（Cantor dust），结果与「生成康托尔尘」相同，完整说明见该工具。去掉中间一格、保留 8 格的版本是谢尔宾斯基地毯。导出 PNG。There is no separate standard definition of a "Sierpinski square". The rule used here, split a square into a 3×3 grid, keep only the four corners and repeat on each, is exactly Cantor dust, the same result as Generate Cantor Dust, which has the full explanation. The version that removes only the centre cell and keeps 8 is the Sierpinski carpet. Export PNG.
如何使用「生成谢尔宾斯基方块」？How do I use the Generate Sierpinski Square tool?
在「生成谢尔宾斯基方块」中，按需设置「宽度」、「高度」、「边距」、「迭代次数」、「背景」等选项，然后点击「绘制」、「下载 PNG」按钮即可。In the Generate Sierpinski Square: Set "Width", "Height", "Padding", "Iterations", "Background", then click "Draw", "Download PNG".
这和康托尔尘有什么区别？How does this differ from Cantor dust?
没有区别：每一步把每个正方形分成 3×3，只保留 4 个角，第 n 次迭代有 4^n 个边长为 1/3^n 的小方块，这就是二维康托尔尘。生成康托尔尘 是这个图形的主页面；保留 8 格（只去掉中心）的是 谢尔宾斯基地毯。There is no difference: at each step every square is split 3×3 and only the 4 corners are kept, so iteration n has 4^n squares of side 1/3^n, which is 2-D Cantor dust. Generate Cantor Dust is the main page for this shape; keeping 8 cells (removing only the centre) gives the Sierpinski carpet.
迭代越多为什么越淡？Why does it fade at higher iterations?
每一步面积只剩 4/9，8 次后约 0.15%，小方块也小于 1 像素，所以几乎看不见；这时页面会提示细节已小于像素。方块用「线条」颜色填实，所以没有单独的「填充」设置。Each step keeps only 4/9 of the area, about 0.15% after 8 steps, and the squares shrink below a pixel, so it almost disappears; the page then notes that the detail is finer than a pixel. The squares are filled in the Line colour, so there is no separate Fill setting.
有哪些选项可以调整？What options can I adjust?
「生成谢尔宾斯基方块」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；「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 Sierpinski Square — "Width" default 512, range 64–2048; "Height" default 512, range 64–2048; "Padding" default 20, range 0–256; "Iterations" default 5, range 1–8; "Background" default #ffffff; "Line" default #1e3a8a. The result always uses the current settings.
「生成谢尔宾斯基方块」免费吗？需要注册吗？Is the Generate Sierpinski Square free? Do I need an account?
「生成谢尔宾斯基方块」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 Sierpinski Square is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.