Ｈ 豪斯多夫分形（H 树）Draw a Hausdorff Fractal
绘制 H 树（豪斯多夫树）：每一步画一个 H 形（或旋转 90° 的工字形），再在它的四个端点上画边长减半、方向转 90° 的同样图形，反复铺满正方形。可调迭代、方向与颜色，导出 PNG。Draw an H-tree (Hausdorff tree): each step draws an H (or the same shape turned 90°, like an I-beam), then a half-size copy turned 90° on each of its four tips, filling a square. Set iterations, orientation and colours; export PNG.
使用说明与常见问题How-to & FAQ
「豪斯多夫分形（H 树）」是什么？What is the Draw a Hausdorff Fractal tool?
绘制 H 树（豪斯多夫树）：每一步画一个 H 形（或旋转 90° 的工字形），再在它的四个端点上画边长减半、方向转 90° 的同样图形，反复铺满正方形。可调迭代、方向与颜色，导出 PNG。Draw an H-tree (Hausdorff tree): each step draws an H (or the same shape turned 90°, like an I-beam), then a half-size copy turned 90° on each of its four tips, filling a square. Set iterations, orientation and colours; export PNG.
如何使用「豪斯多夫分形（H 树）」？How do I use the Draw a Hausdorff Fractal tool?
在「豪斯多夫分形（H 树）」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。Set the canvas "Width" and "Height", the "Padding" around the drawing and the "Line width", choose the number of "Iterations" and the "Orientation" (vertical or horizontal first), pick the "Background", "Line" and "Fill" colours, then click "Draw". "Download PNG" saves the picture at the canvas size.
H 树为什么能铺满平面？Why does the H-tree fill the plane?
每一步长度减半、分支加倍，极限点集在正方形内稠密，只留下少数永远到不了的点。Length halves and branches double each step; in the limit the points are dense in a square, missing only a few unreachable spots.
竖/横方向有什么差别？Vertical vs horizontal first?
“先横后竖”第一层是横梁加两端竖线的 H 形；“先竖后横”第一层是竖线加两端横线的工字形。之后每层都在四个端点上画转 90° 的半尺寸图形，所以两者整体是同一结构旋转 90°。"Horizontal first" starts with an H (a crossbar with uprights at both ends); "Vertical first" starts with the same shape turned 90° (an upright with bars at both ends, like an I-beam). Every later level puts a half-size copy turned 90° on the four tips, so the two results are the same structure rotated by 90°.
有哪些选项可以调整？What options can I adjust?
「豪斯多夫分形（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；「迭代次数」默认 5，范围 1–9；「方向」可选 先竖后横、先横后竖（默认 先竖后横）；「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 Hausdorff 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; "Iterations" default 5, range 1–9; "Orientation": Vertical first, Horizontal first (default Vertical first); "Background" default #ffffff; "Line" default #1e3a8a. Changing any option regenerates the result with the new setting.
「豪斯多夫分形（H 树）」免费吗？需要注册吗？Is the Draw a Hausdorff Fractal free? Do I need an account?
「豪斯多夫分形（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 Draw a Hausdorff 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.