Ｈ 生成 H 分形（H 树）Generate H Fractal

使用说明与常见问题How-to & FAQ

「生成 H 分形（H 树）」是什么？What is the Generate H Fractal tool?

生成 H 树分形。可调迭代，导出 PNG。可设置「宽度」、「高度」、「边距」、「线宽」、「层数」。Generate an H-tree fractal. Set iterations; export PNG. Settings: Width, Height, Padding, Line width, Levels.

如何使用「生成 H 分形（H 树）」？How do I use the Generate H Fractal tool?

在「生成 H 分形（H 树）」中，按需设置「宽度」、「高度」、「边距」、「线宽」、「层数」等选项，然后点击「绘制」、「下载 PNG」按钮即可。In the Generate H Fractal: Set "Width", "Height", "Padding", "Line width", "Levels", then click "Draw", "Download PNG".

H 树是怎样画的？How is the H-tree drawn?

第 1 层是一条横线；之后在上一层每条线段的两个端点处，各画一条与它垂直、长度为它 1/√2 的线段，横竖交替。这样第 n 层共有 2^n − 1 条线段，第 2 层组成字母 H，各层线段互不重叠，层数增加时逐渐铺满一个长宽比 √2 的矩形。Level 1 is one horizontal segment. At each later level, a segment 1/√2 as long and perpendicular to its parent is centred on each endpoint of every segment from the previous level, alternating horizontal and vertical. Level n has 2^n − 1 segments in total, level 2 forms the letter H, the segments never overlap, and more levels gradually fill a rectangle with aspect ratio √2.

和「绘制豪斯多夫分形」有什么关系？How does it relate to Draw a Hausdorff Fractal?

H 树常用来说明豪斯多夫维数为 2 的平面填充：线段总长无限增长，却始终是一棵不自交的树。本页只画标准 H 树；层数上限 14（16383 条线段），更细的层已小于一个像素。The H-tree is a common example of a plane-filling shape with Hausdorff dimension 2: the total length grows without bound while it stays a tree that never crosses itself. This page draws only the standard H-tree; the limit is 14 levels (16,383 segments), beyond which the segments are smaller than a pixel.

有哪些选项可以调整？What options can I adjust?

「生成 H 分形（H 树）」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；「层数」默认 9，范围 1–14；「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 H 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; "Levels" default 9, range 1–14; "Background" default #ffffff; "Line" default #1e3a8a. The result always uses the current settings.

「生成 H 分形（H 树）」免费吗？需要注册吗？Is the Generate H Fractal free? Do I need an account?

「生成 H 分形（H 树）」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 H 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.