⬡ 生成谢尔宾斯基六边形Generate Sierpinski Hexagon
生成谢尔宾斯基六边形：把六边形换成六个 1/3 大小、位于各个角上的小六边形（中间留空），反复迭代。导出 PNG。Generate the Sierpinski hexagon: each hexagon is replaced by six copies at 1/3 size placed at its corners, leaving the centre empty, repeated. Export PNG.
使用说明与常见问题How-to & FAQ
「生成谢尔宾斯基六边形」是什么？What is the Generate Sierpinski Hexagon tool?
生成谢尔宾斯基六边形：把六边形换成六个 1/3 大小、位于各个角上的小六边形（中间留空），反复迭代。导出 PNG。Generate the Sierpinski hexagon: each hexagon is replaced by six copies at 1/3 size placed at its corners, leaving the centre empty, repeated. Export PNG.
如何使用「生成谢尔宾斯基六边形」？How do I use the Generate Sierpinski Hexagon tool?
在「生成谢尔宾斯基六边形」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 Hexagon: Set "Width", "Height", "Padding", "Iterations", "Background", then click "Draw", "Download PNG".
结构是怎样的？What is the structure?
每一步把每个六边形换成 6 个边长为 1/3 的小六边形，分别放在原六边形的 6 个角上，正中间留空；相邻的小六边形只在一点相接。第 n 次迭代共有 6^n 个六边形，外轮廓逐渐接近科赫雪花。At each step every hexagon is replaced by 6 hexagons with 1/3 the side, one at each of its 6 corners, leaving the centre empty; neighbouring small hexagons touch only at a point. Iteration n has 6^n hexagons and the outline approaches the Koch snowflake.
和谢尔宾斯基三角形有什么关系？How does it relate to the Sierpinski triangle?
思想相同：只保留角上的缩小副本、去掉中间。三角形保留 3 个 1/2 大小的副本，这里保留 6 个 1/3 大小的副本；它也等于去掉中心块的六边形雪花（hexaflake）。Same idea: keep shrunken copies at the corners and drop the middle. The triangle keeps 3 copies at 1/2 size; this keeps 6 copies at 1/3 size. It is also the hexaflake without its centre hexagon.
颜色怎么设置？How do I set the colour?
六边形用「线条」颜色填实，背景用「背景」颜色；这个图形没有单独的轮廓，所以页面不提供「填充」设置。The hexagons are filled solid in the Line colour on the Background colour; the shape has no separate outline, so there is no Fill setting.
有哪些选项可以调整？What options can I adjust?
「生成谢尔宾斯基六边形」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；「迭代次数」默认 4，范围 1–6；「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 Hexagon — "Width" default 512, range 64–2048; "Height" default 512, range 64–2048; "Padding" default 20, range 0–256; "Iterations" default 4, range 1–6; "Background" default #ffffff; "Line" default #1e3a8a. The result always uses the current settings.
「生成谢尔宾斯基六边形」免费吗？需要注册吗？Is the Generate Sierpinski Hexagon free? Do I need an account?
「生成谢尔宾斯基六边形」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 Generate Sierpinski Hexagon is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.