⬡ 生成戈斯珀曲线Generate Gosper Curve

使用说明与常见问题How-to & FAQ

「生成戈斯珀曲线」是什么？What is the Generate Gosper Curve tool?

生成戈斯珀流蛇曲线。可调迭代，导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「迭代次数」。Generate the Gosper flowsnake. Set iterations; export PNG. Settings: Width, Height, Padding, Line width, Iterations.

如何使用「生成戈斯珀曲线」？How do I use the Generate Gosper Curve tool?

在「生成戈斯珀曲线」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 Gosper Curve: Set "Width", "Height", "Padding", "Line width", "Iterations", then click "Draw", "Download PNG".

戈斯珀曲线有何特点？What is special about the Gosper curve?

它是六边形格子上的空间填充曲线，俗称“流蛇”（flowsnake）：每一步把每条线段换成 7 条更短的线段，曲线从不重复走同一条边，迭代越多越接近填满一个类似雪花的区域。It is a space-filling curve on a hexagonal grid, nicknamed the flowsnake: each step replaces every segment with 7 shorter ones, the curve never runs along the same edge twice, and higher iterations fill a snowflake-like region.

用的是什么规则？Which rule does it use?

L 系统 A → A-B--B+A++AA+B-，B → +A-BB--B-A++A+B，转角 60°，与「绘制流蛇分形」使用同一套规则。6 次迭代约有 11.8 万条线段，已接近实心。The L-system A → A-B--B+A++AA+B-, B → +A-BB--B-A++A+B with 60° turns, the same rule as Draw a Flowsnake Fractal. Six iterations give about 118,000 segments and look nearly solid.

有哪些选项可以调整？What options can I adjust?

「生成戈斯珀曲线」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；「迭代次数」默认 4，范围 1–6；「背景」默认 #ffffff；「线条」默认 #1e3a8a。每次生成结果都按当前设置处理。Settings in the Generate Gosper Curve — "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 1–6; "Background" default #ffffff; "Line" default #1e3a8a. The result always uses the current settings.

「生成戈斯珀曲线」免费吗？需要注册吗？Is the Generate Gosper Curve free? Do I need an account?

「生成戈斯珀曲线」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 Generate Gosper Curve is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.