❄ 生成科赫雪花Generate Koch Snowflake

使用说明与常见问题How-to & FAQ

「生成科赫雪花」是什么？What is the Generate Koch Snowflake tool?

生成经典科赫雪花。导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the classic Koch snowflake. Export PNG. Settings: Width, Height, Padding, Line width, Iterations.

如何使用「生成科赫雪花」？How do I use the Generate Koch Snowflake tool?

在「生成科赫雪花」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 Koch Snowflake: Set "Width", "Height", "Padding", "Line width", "Iterations", then click "Draw", "Download PNG".

周长和面积怎样变化？How do the perimeter and area change?

每次迭代把每条边换成 4 段、每段长 1/3，所以周长每步乘 4/3，无限迭代后周长趋于无穷；尖角向外凸，第 1 次迭代是六角星，面积是原三角形的 4/3，极限是原三角形面积的 8/5，始终有限。Each iteration replaces every edge with 4 pieces a third as long, so the perimeter is multiplied by 4/3 each step and grows without bound. The spikes point outward: iteration 1 is a six-pointed star with 4/3 of the triangle's area, and the area tends to 8/5 of the triangle — always finite.

填充色怎么用？How is the fill colour used?

雪花内部用「填充」颜色涂满，轮廓用「线条」颜色描边；想只看轮廓，可把填充设成与背景相同。迭代 0–6 次，6 次时每条边已有 4096 段。The inside is painted with the Fill colour and the outline drawn in the Line colour; for an outline only, set Fill to the background colour. Iterations go from 0 to 6; at 6 each edge already has 4,096 pieces.

有哪些选项可以调整？What options can I adjust?

「生成科赫雪花」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；「线宽」默认 2，范围 0.5–40；「迭代次数」默认 4，范围 0–6；「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 Koch Snowflake — "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 4, range 0–6; "Background" default #ffffff; "Line" default #1e3a8a; "Fill" default #93c5fd. The result always uses the current settings.

「生成科赫雪花」免费吗？需要注册吗？Is the Generate Koch Snowflake free? Do I need an account?

「生成科赫雪花」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 Koch Snowflake is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.