希尔伯特曲线

功能说明What It Does

希尔伯特曲线是一种空间填充曲线,能用一条连续折线经过正方形区域内所有格点。本工具按阶数递归生成 4ⁿ 个节点并用折线连接,支持彩虹渐变或单色、网格与节点标记,导出透明 PNG。

The Hilbert curve is a space-filling curve that visits every point of a grid in one continuous polyline. This tool generates 4ⁿ nodes recursively by order, links them, supports gradient or solid colors plus grid and node markers, and exports a transparent PNG.

全部在浏览器本地完成,数据不会上传。

Everything runs locally in your browser - nothing is uploaded.

阶数说明About the order

阶数 n 对应边长 2ⁿ、节点数 4ⁿ。1 阶是 2×2 的「门」形,2 阶 4×4,每加一阶曲线细分一层。8 阶含 65536 个节点,已接近填充整个平面。

Order n gives a 2ⁿ by 2ⁿ grid with 4ⁿ nodes. Order 1 is a 2×2 "U" shape, order 2 is 4×4 - each level subdivides once. Order 8 has 65,536 nodes, nearly filling the plane.

使用步骤How to Use

1. 调整阶数(1-8),观察曲线逐级细分。Adjust the order (1-8) to see the curve subdivide.
2. 选择渐变 / 单色、粗细、网格与节点。Pick gradient or solid, thickness, grid and nodes.
3. 满意后「导出PNG」。Click "Export PNG" when happy.

常见问题FAQ