希尔伯特曲线

Conclusion

n 阶的希尔伯特曲线是从 [0,1] 区间到[0,1]×[0,1]平面区域的映射 , 把 0 和1 映射到区域左下角和右下角: (0)=(0,0), (0)=(1,0) 并且, 通过适当的调整,让每个1/4的小区间映射到4个区域内. 填充整个区域的希尔伯特曲线是这样的函数 f, 使得函数列 fn逐点收敛到它. 即: ( ):=lim →∞ ( )

Image

this picture explains a line refer to a point in the image. x, y point a point in the map, t means how long this point in [0,1] line.

Video

this video about how produce a Hilbert curve.

其构造方式是把前一阶的曲线复制四份, 将左下角和右下角的曲线做一个沿对角线的翻转, 然后增加三条线段把这四份连起来.

and how apply it in real world.

Refer

wiki：https://en.wikipedia.org/wiki/Hilbert_curve image from：http://bit-player.org/extras/hilbert/

Apply

• Using Hilbert for shuffle data:https://www.moderndescartes.com/essays/shuffle_viz/

• Using observablehq to make shuffle visualable :https://observablehq.com/@mbostock/visualizing-order

• visual in Codepen：https://codepen.io/search/pens?q=Hilbert
  

• Realized by different program languages：https://rosettacode.org/wiki/Hilbert_curve