⬜ 生成二次科赫岛Generate Quadratic Koch Island
生成二次科赫岛（方版科赫，转角 90°）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a quadratic Koch island (square Koch with 90° turns). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
使用说明与常见问题How-to & FAQ
「生成二次科赫岛」是什么？What is the Generate Quadratic Koch Island tool?
生成二次科赫岛（方版科赫，转角 90°）。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate a quadratic Koch island (square Koch with 90° turns). Export PNG. Settings: Width, Height, Padding, Line width, Iterations.
如何使用「生成二次科赫岛」？How do I use the Generate Quadratic Koch Island tool?
在「生成二次科赫岛」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。In the Generate Quadratic Koch Island: Set "Width", "Height", "Padding", "Line width", "Iterations", then click "Draw", "Download PNG".
二次科赫岛是怎么生成的？How is the quadratic Koch island made?
从正方形出发，把每条边替换成生成元 F → F+F-F-FF+F+F-F（转角 90°），每次迭代边数乘 8、边长缩为 1/4，所以面积保持不变而周长不断变长，轮廓呈方形的锯齿岛。Start from a square and replace every side with the generator F → F+F-F-FF+F+F-F (90° turns). Each iteration multiplies the number of sides by 8 and shrinks them to 1/4, so the area stays the same while the perimeter keeps growing, giving a square, notched island.
「填充」有什么用？What does Fill do?
岛是闭合轮廓：「填充」颜色（默认 #93c5fd）会涂满岛的内部，再用「线条」颜色描边；把填充设成与背景相同的颜色就只剩轮廓。The island is a closed outline: the Fill colour (default #93c5fd) paints its interior, then the Line colour draws the border. Set Fill to the background colour to see only the outline.
边数？Sides?
外框四边各做科赫迭代。All four outer sides are Koch-iterated.
有哪些选项可以调整？What options can I adjust?
「生成二次科赫岛」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 0–5；「背景」默认 #ffffff；「线条」默认 #1e3a8a；「填充」默认 #93c5fd。每次生成结果都按当前设置处理。Settings in the Generate Quadratic Koch Island — "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 0–5; "Background" default #ffffff; "Line" default #1e3a8a; "Fill" default #93c5fd. The result always uses the current settings.
「生成二次科赫岛」免费吗？需要注册吗？Is the Generate Quadratic Koch Island free? Do I need an account?
「生成二次科赫岛」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 Quadratic Koch Island is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.