❅ 三片雪花分形（谢尔宾斯三角形变体）Draw a Triflake Fractal
绘制三片雪花（triflake，也就是 n=3 的多边形雪花 n-flake）：把等边三角形换成三个边长一半、各占一个角的三角形，中间留出倒三角空洞，反复迭代就得到谢尔宾斯基三角形。可调迭代（1–8）与颜色，导出 PNG。Draw a triflake (the n-flake with n = 3): an equilateral triangle is replaced by three half-size triangles, one in each corner, leaving an upside-down triangular hole in the middle; iterating gives the Sierpiński triangle. Set iterations (1–8) and colours; export PNG.
使用说明与常见问题How-to & FAQ
「三片雪花分形（谢尔宾斯三角形变体）」是什么？What is the Draw a Triflake Fractal tool?
绘制三片雪花（triflake，也就是 n=3 的多边形雪花 n-flake）：把等边三角形换成三个边长一半、各占一个角的三角形，中间留出倒三角空洞，反复迭代就得到谢尔宾斯基三角形。可调迭代（1–8）与颜色，导出 PNG。Draw a triflake (the n-flake with n = 3): an equilateral triangle is replaced by three half-size triangles, one in each corner, leaving an upside-down triangular hole in the middle; iterating gives the Sierpiński triangle. Set iterations (1–8) and colours; export PNG.
如何使用「三片雪花分形（谢尔宾斯三角形变体）」？How do I use the Draw a Triflake Fractal tool?
在「三片雪花分形（谢尔宾斯三角形变体）」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.
triflake 是什么？What is a triflake?
triflake 是边数为 3 的多边形雪花（n-flake）：每个三角形换成 3 个边长一半的角三角形，中间去掉一个倒三角。第 n 次迭代共有 3ⁿ⁻¹ 个小三角形，极限图形就是谢尔宾斯基三角形，分形维数 log 3 / log 2 ≈ 1.585。A triflake is the polygon flake (n-flake) with 3 sides: every triangle becomes 3 half-size corner triangles and the upside-down middle triangle is removed. Iteration n has 3ⁿ⁻¹ small triangles, and the limit is the Sierpiński triangle, with fractal dimension log 3 / log 2 ≈ 1.585.
和科赫雪花、五片/六片雪花有什么关系？How does it relate to the Koch snowflake and penta/hexaflake?
科赫雪花是在边上加尖角的曲线，和这里不同；triflake、pentaflake、hexaflake 都属于 n-flake 家族，只是边数分别为 3、5、6。五边形和六边形版本还会在中心多放一块，三角形版本不放。The Koch snowflake adds spikes along the edges, which is a different construction. Triflake, pentaflake and hexaflake all belong to the n-flake family with 3, 5 and 6 sides; the pentagon and hexagon versions also keep a centre piece, the triangle version does not.
有哪些选项可以调整？What options can I adjust?
「三片雪花分形（谢尔宾斯三角形变体）」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 1–8；「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 Triflake 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 5, range 1–8; "Background" default #ffffff; "Line" default #1e3a8a; "Fill" default #93c5fd. Changing any option regenerates the result with the new setting.
「三片雪花分形（谢尔宾斯三角形变体）」免费吗？需要注册吗？Is the Draw a Triflake Fractal free? Do I need an account?
「三片雪花分形（谢尔宾斯三角形变体）」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 Triflake 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.