ℤ 莫顿分形（Z 阶曲线）Draw a Morton Fractal

使用说明与常见问题How-to & FAQ

「莫顿分形（Z 阶曲线）」是什么？What is the Draw a Morton Fractal tool?

绘制莫顿 Z 阶曲线：按位交错遍历网格的空间填充折线，可调阶数与颜色，导出 PNG。Draw the Morton Z-order curve: a space-filling polyline from bit-interleaved grid traversal. Set order and colours; export PNG.

如何使用「莫顿分形（Z 阶曲线）」？How do I use the Draw a Morton Fractal tool?

在「莫顿分形（Z 阶曲线）」中，按需设置「宽度」、「高度」、「边距」、「线宽」、「阶数」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 the curve "Order", pick the "Background", "Line" and "Fill" colours, then click "Draw". "Download PNG" saves the picture at the canvas size.

Z 阶曲线有什么用？What is Z-order used for?

数据库与图形里用它把二维坐标编成一维键，让邻近点在键上也较近。Databases and graphics encode 2-D coordinates into a 1-D key so nearby points stay fairly near in the key.

阶数 8 会有多密？How dense is order 8?

256×256 = 65536 个点连成折线，已经很密；更高会明显变慢。256×256 = 65,536 points on the polyline — already dense; higher is slower.

有哪些选项可以调整？What options can I adjust?

「莫顿分形（Z 阶曲线）」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；「阶数」默认 5，范围 1–8；「背景」默认 #ffffff；「线条」默认 #1e3a8a。改动任一选项后结果会按新设置重新生成。Settings in the Draw a Morton 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; "Order" default 5, range 1–8; "Background" default #ffffff; "Line" default #1e3a8a. Changing any option regenerates the result with the new setting.

「莫顿分形（Z 阶曲线）」免费吗？需要注册吗？Is the Draw a Morton Fractal free? Do I need an account?

「莫顿分形（Z 阶曲线）」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 Draw a Morton 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.