✪ 五片雪花分形Draw a Pentaflake Fractal
绘制五边形雪花（pentaflake）：在大正五边形的五个角上各摆一个更小的五边形，中心再放一个倒置的小五边形，六块互相接触但不重叠，反复迭代。可调迭代（1–5）与颜色，导出 PNG。Draw a pentaflake: a smaller pentagon in each of the five corners of a larger one plus an upside-down one in the centre, all six touching without overlapping, iterated. Set iterations (1–5) and colours; export PNG.
使用说明与常见问题How-to & FAQ
「五片雪花分形」是什么？What is the Draw a Pentaflake Fractal tool?
绘制五边形雪花（pentaflake）：在大正五边形的五个角上各摆一个更小的五边形，中心再放一个倒置的小五边形，六块互相接触但不重叠，反复迭代。可调迭代（1–5）与颜色，导出 PNG。Draw a pentaflake: a smaller pentagon in each of the five corners of a larger one plus an upside-down one in the centre, all six touching without overlapping, iterated. Set iterations (1–5) and colours; export PNG.
如何使用「五片雪花分形」？How do I use the Draw a Pentaflake Fractal tool?
在「五片雪花分形」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。Set the canvas "Width" and "Height", the "Padding" around the drawing and the "Line width", choose how many "Iterations" to draw, pick the "Background", "Line" and "Fill" colours, then click "Draw". "Download PNG" saves the picture at the canvas size.
缩放比为什么是这个？Why this scale factor?
每一步把五边形换成 6 个缩小到 1/(1+2cos 36°) ≈ 0.382 倍的五边形：五个角各 1 个（角上那块的顶点与原顶点重合，方向与原五边形相同），中心 1 个倒置（旋转 180°），它的五条边分别贴着五个角块的内侧边。按这个比例它们互相接触但不重叠，之间留出的空隙就是五片雪花的镂空。只画最后一层，所以空隙清楚可见。Each step replaces a pentagon with 6 pentagons scaled by 1/(1+2cos 36°) ≈ 0.382: one in each corner (its vertex on the original vertex, same orientation as the original) and one in the centre turned upside down (rotated 180°), whose five edges sit against the inner edges of the five corner pieces. At that ratio they touch without overlapping, and the gaps between them are the pentaflake's holes. Only the last level is drawn, so the gaps stay visible.
迭代上限为什么是 5？Why max 5 iterations?
第 n 次正好有 6ⁿ⁻¹ 个五边形（结果下方会显示数量），5 次是 1296 个；再往上会小于像素，看不出更多细节。Iteration n has exactly 6ⁿ⁻¹ pentagons (the count is shown below the drawing), so 5 means 1,296; beyond that they shrink below a pixel and show no more detail.
有哪些选项可以调整？What options can I adjust?
「五片雪花分形」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；「线宽」默认 2，范围 0.5–40；「迭代次数」默认 3，范围 1–5；「背景」默认 #ffffff；「线条」默认 #1e3a8a；「填充」默认 #93c5fd。改动任一选项后结果会按新设置重新生成。Settings in the Draw a Pentaflake Fractal — "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 3, range 1–5; "Background" default #ffffff; "Line" default #1e3a8a; "Fill" default #93c5fd. Changing any option regenerates the result with the new setting.
「五片雪花分形」免费吗？需要注册吗？Is the Draw a Pentaflake Fractal free? Do I need an account?
「五片雪花分形」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 Draw a Pentaflake Fractal is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.