🧊 冰晶分形（弗罗斯蒂）Draw a Frosty Fractal

使用说明与常见问题How-to & FAQ

「冰晶分形（弗罗斯蒂）」是什么？What is the Draw a Frosty Fractal tool?

绘制冰晶风分形（Cesàro 折线）：类似科赫曲线，但把 60° 的尖角换成可调的折角（默认 90° 直角），形成霜花般的折线。可调迭代（1–9）与折角（10–170°），导出 PNG。Draw a frosty ice fractal (Cesàro polyline): Koch-like, but the 60° spike becomes an adjustable fold (90° right angle by default) for a frost-like zigzag. Set iterations (1–9) and fold angle (10–170°); export PNG.

如何使用「冰晶分形（弗罗斯蒂）」？How do I use the Draw a Frosty Fractal tool?

在「冰晶分形（弗罗斯蒂）」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 "Fold angle (°)", pick the "Background", "Line" and "Fill" colours, then click "Draw". "Download PNG" saves the picture at the canvas size.

和科赫雪花有什么不同？How is this different from Koch?

科赫用 60°；冰晶默认 90°（Cesàro），折角更陡，看起来像霜花或闪电。Koch uses 60°; frosty defaults to 90° (Cesàro) for steeper folds like frost or lightning.

折角怎么影响形状？为什么最多 9 次？How does the fold angle change the shape, and why at most 9 iterations?

折角是每次转向的角度：90° 是经典 Cesàro 直角折线；角度越大折线越往回折、越挤成一团（170° 时几乎原路折返），越小越接近直线。每迭代一次线段数 ×4，9 次已有 4⁹ = 262,144 段；再多会让浏览器长时间无响应，所以超过 9 会直接提示。The fold angle is the turn at each bend: 90° gives the classic Cesàro right-angle zigzag; larger angles fold the line back on itself into a tighter tangle (170° almost retraces itself), smaller ones flatten it toward a straight line. Each iteration multiplies the segments by 4, so 9 already means 4⁹ = 262,144 segments; more would freeze the browser, so anything above 9 shows a message instead.

有哪些选项可以调整？What options can I adjust?

「冰晶分形（弗罗斯蒂）」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 7，范围 1–9；「折角（°）」默认 90，范围 10–170；「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 Frosty 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 7, range 1–9; "Fold angle (°)" default 90, range 10–170; "Background" default #ffffff; "Line" default #1e3a8a. Changing any option regenerates the result with the new setting.

「冰晶分形（弗罗斯蒂）」免费吗？需要注册吗？Is the Draw a Frosty Fractal free? Do I need an account?

「冰晶分形（弗罗斯蒂）」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 Frosty 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.