Hilbert curve

In mathematics, the Hilbert curve is a continuous curve - comes arbitrarily close to any point of a square area and the area completely fills - by repeating their construction process. The Hilbert curve is a so-called space-filling or FASS - curve. It was discovered in 1891 by the German mathematician David Hilbert. The ability to completely cover a two-dimensional field with a steady one-dimensional curve, was the mathematicians of the nineteenth century new ( see also monster curve).

The Euclidean length of the curve, i.e., grows exponentially with. Your Hausdorff dimension is due to the property to be a space-filling curve, exactly 2

With the development of space-filling curves, such as parallel computers, the Hilbert curve receive a possible application, by being used for the determination of the load distribution of the individual processors.

Hilbert curves 1st and 2nd order

Hilbert curves 1st to 3rd order

3D Hilbert curves 1st to 3rd order

Also in higher dimensions can generate Hilbert curves. Thus, it is possible with a continuous one-dimensional graph, for example, a three-dimensional space can be completely covered. The folding of the genome resembles a three-dimensional Hilbert curve.