✦ 生成谢尔宾斯基多边雪花Generate Sierpinski Polyflake
在正多边形顶点上迭代谢尔宾斯基式缩放。导出 PNG。可设置「宽度」、「高度」、「边距」、「迭代次数」、「边数」。Iterate Sierpinski-style scaling on a regular polygon vertices. Export PNG. Settings: Width, Height, Padding, Iterations, Sides.
使用说明与常见问题How-to & FAQ
「生成谢尔宾斯基多边雪花」是什么？What is the Generate Sierpinski Polyflake tool?
在正多边形顶点上迭代谢尔宾斯基式缩放。导出 PNG。可设置「宽度」、「高度」、「边距」、「迭代次数」、「边数」。Iterate Sierpinski-style scaling on a regular polygon vertices. Export PNG. Settings: Width, Height, Padding, Iterations, Sides.
如何使用「生成谢尔宾斯基多边雪花」？How do I use the Generate Sierpinski Polyflake tool?
在「生成谢尔宾斯基多边雪花」中，按需设置「宽度」、「高度」、「边距」、「迭代次数」、「边数」等选项，然后点击「绘制」、「下载 PNG」按钮即可。In the Generate Sierpinski Polyflake: Set "Width", "Height", "Padding", "Iterations", "Sides", then click "Draw", "Download PNG".
缩放比例怎么定？How is the scale chosen?
这是去掉中心的 n 边形雪花（n-flake）：每个多边形换成 N 个副本，各自贴在一个顶点上，缩放比 r = 1 / (2·(1 + Σ cos(2πk/N)))（k = 1…⌊N/4⌋），这样相邻副本恰好只在一点相接、互不重叠。N=3 时 r = 1/2，就是谢尔宾斯基三角形；N=5 时 r ≈ 0.382（五边形）；N=6 时 r = 1/3（六边形）；N=4 时 r = 1/2，四个副本正好铺满正方形。This is the n-flake without its centre: each polygon is replaced by N copies, one in each corner, scaled by r = 1 / (2·(1 + Σ cos(2πk/N))) for k = 1…⌊N/4⌋, so that neighbouring copies touch at exactly one point and never overlap. N = 3 gives r = 1/2, the Sierpinski triangle; N = 5 gives r ≈ 0.382 (the pentagon); N = 6 gives r = 1/3 (the hexagon); N = 4 gives r = 1/2, where the four copies tile the square exactly.
会超出画布吗？颜色怎么设？Can it run off the canvas? How do I set the colour?
不会。外轮廓始终就是第一个多边形，整体按它缩放到留白边距之内。多边形用「线条」颜色填实，所以没有单独的「填充」设置。No. The outer outline is always the first polygon, and the drawing is scaled so that it fits inside the padding. The polygons 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?
「生成谢尔宾斯基多边雪花」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 3，范围 1–5；「边数」默认 6，范围 3–10；「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 Polyflake — "Width" default 512, range 64–2048; "Height" default 512, range 64–2048; "Padding" default 20, range 0–256; "Iterations" default 3, range 1–5; "Sides" default 6, range 3–10; "Background" default #ffffff; "Line" default #1e3a8a. The result always uses the current settings.
「生成谢尔宾斯基多边雪花」免费吗？需要注册吗？Is the Generate Sierpinski Polyflake free? Do I need an account?
「生成谢尔宾斯基多边雪花」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 Polyflake is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.