Mathematics · Study 044
Hilbert Curve
Watch a Hilbert curve thread through every cell of a grid without lifting the pen, from order 2 up to order 7 and 16,384 cells.
What you're looking at
The curve of order n visits each cell of a 2 to the n by 2 to the n grid exactly once, moving only to adjacent cells. Each order is built from four copies of the previous one, two of them rotated, joined by three short links. The red dot is the pen.
The idea behind it
David Hilbert published the construction in 1891 to show that a continuous line can pass through every point of a square. It has a practical afterlife: because points close together on the curve are close together in the square, databases and image formats use it to map two dimensional data onto a one dimensional index.
Try this
Watch each order draw itself. Restart to begin again from the simplest curve.
