Generate the space-filling Hilbert fractal curve - adjustable order & colors, export PNG
Recursively generate the space-filling Hilbert curve - adjust order 1-8, rainbow gradient or solid, optional grid and node markers, export transparent PNG. All local, nothing uploaded.
了解分形原理、阶数与常见问题。Fractal basics, order levels, and answers to common questions.
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 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.
不会。希尔伯特曲线是自避免的:每个格点恰好经过一次,折线不相交。No - the Hilbert curve is self-avoiding: every grid point is visited exactly once, with no crossings.
8 阶 65536 节点本地绘制流畅,渐变按段批量上色,不会卡顿。Order 8 (65K nodes) renders smoothly locally; gradients are batched by segment.
建议 1-4 阶显示节点;高阶节点过密,建议关闭以保持清晰。Use node markers for orders 1-4; at high orders they get too dense - keep them off.
