❄️ 科赫分形（雪花 / 反雪花 / 折线）Draw a Koch Fractal
绘制科赫分形：雪花（外凸）、反雪花（内凹）或单条科赫折线。可调迭代、画布、线宽、填充与方向，导出 PNG，本地完成。Draw a Koch fractal: snowflake (outward), anti-snowflake (inward) or a single Koch polyline. Set iterations, canvas, line width, fill and orientation; export PNG locally.
使用说明与常见问题How-to & FAQ
「科赫分形（雪花 / 反雪花 / 折线）」是什么？What is the Draw a Koch Fractal tool?
绘制科赫分形：雪花（外凸）、反雪花（内凹）或单条科赫折线。可调迭代、画布、线宽、填充与方向，导出 PNG，本地完成。Draw a Koch fractal: snowflake (outward), anti-snowflake (inward) or a single Koch polyline. Set iterations, canvas, line width, fill and orientation; export PNG locally.
如何使用「科赫分形（雪花 / 反雪花 / 折线）」？How do I use the Draw a Koch Fractal tool?
在「科赫分形（雪花 / 反雪花 / 折线）」中，按需设置「宽度」、「高度」、「边距」、「线宽」、「类型」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 the "Type" (snowflake, anti-snowflake or a single Koch line), the number of "Iterations" and the "Orientation", pick the "Background", "Line" and "Fill" colours, then click "Draw". "Download PNG" saves the picture at the canvas size.
三种类型怎么选？Which type should I pick?
雪花从等边三角形向外长出尖角；反雪花向内凹，迭代后像许多小岛；折线只画一条科赫曲线。Snowflake grows spikes outward from an equilateral triangle; anti-snowflake folds inward into island shapes; the line is a single Koch curve.
迭代次数建议？How many iterations?
3–5 次细节已经很丰富；7 次线段极多，大画布上会慢一些。3–5 already looks rich; 7 has very many segments and can be slower on large canvases.
有哪些选项可以调整？What options can I adjust?
「科赫分形（雪花 / 反雪花 / 折线）」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；「类型」可选 雪花（外凸）、反雪花（内凹）、科赫折线（默认 雪花（外凸））；「迭代次数」默认 4，范围 0–7；「方向」可选 尖朝上、尖朝下、朝左、朝右（默认 尖朝上）；「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 Koch 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; "Type": Snowflake, Anti-snowflake, Koch line (default Snowflake); "Iterations" default 4, range 0–7; "Orientation": Tip up, Tip down, Left, Right (default Tip up); "Background" default #ffffff; "Line" default #1e3a8a; "Fill" default #93c5fd. Changing any option regenerates the result with the new setting.
「科赫分形（雪花 / 反雪花 / 折线）」免费吗？需要注册吗？Is the Draw a Koch Fractal free? Do I need an account?
「科赫分形（雪花 / 反雪花 / 折线）」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 Koch 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.