Ｖ V 分形（二叉 V 树）Draw a V-Fractal
绘制二叉 V 分形：从底部一点向上张开一个 V，每条臂的末端再长出缩小到 0.7 倍的同样 V，形成对称的二叉树。可调迭代（1–10）、张角（10–80°）与颜色，导出 PNG。Draw a binary V-fractal: a V opens upward from a base point, and the tip of each arm grows the same V scaled by 0.7, forming a symmetric binary tree. Set iterations (1–10), opening angle (10–80°) and colours; export PNG.
使用说明与常见问题How-to & FAQ
「V 分形（二叉 V 树）」是什么？What is the Draw a V-Fractal tool?
绘制二叉 V 分形：从底部一点向上张开一个 V，每条臂的末端再长出缩小到 0.7 倍的同样 V，形成对称的二叉树。可调迭代（1–10）、张角（10–80°）与颜色，导出 PNG。Draw a binary V-fractal: a V opens upward from a base point, and the tip of each arm grows the same V scaled by 0.7, forming a symmetric binary tree. Set iterations (1–10), opening angle (10–80°) and colours; export PNG.
如何使用「V 分形（二叉 V 树）」？How do I use the Draw a V-Fractal tool?
在「V 分形（二叉 V 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 "Opening angle (°)", pick the "Background", "Line" and "Fill" colours, then click "Draw". "Download PNG" saves the picture at the canvas size.
V 分形的结构？How is a V-fractal built?
第 1 次从底部一点画出两条臂组成的 V（两臂夹角就是张角），之后每条臂的末端再画一个臂长 ×0.7 的 V，方向沿着这条臂继续张开。n 次迭代共有 2ⁿ⁺¹−2 段，整棵树会自动缩放到画布内。Iteration 1 draws a V of two arms from a base point (the angle between the arms is the opening angle); then the tip of every arm grows a V with arms ×0.7 as long, opening along that arm. n iterations give 2ⁿ⁺¹−2 segments, and the whole tree is scaled to fit the canvas.
张角太大会怎样？What if the opening angle is large?
张角越大树越宽，分支越早相互交叉；小张角像细高的树。张角须在 10–80° 之间，超出范围或留空会提示，不会自动改值。A larger angle makes a wider tree whose branches cross sooner; a small angle looks like a tall thin tree. The angle must be 10–80°; values outside that range or an empty box show a message instead of being changed silently.
有哪些选项可以调整？What options can I adjust?
「V 分形（二叉 V 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 6，范围 1–10；「张角（°）」默认 45，范围 10–80；「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 V-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 6, range 1–10; "Opening angle (°)" default 45, range 10–80; "Background" default #ffffff; "Line" default #1e3a8a. Changing any option regenerates the result with the new setting.
「V 分形（二叉 V 树）」免费吗？需要注册吗？Is the Draw a V-Fractal free? Do I need an account?
「V 分形（二叉 V 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 V-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.