Hilbert curve

Both the true Hilbert curve and its discrete approximations are useful because they give a mapping between 1D and 2D space that preserves locality fairly well.

For example, the range of IP addresses used by computers can be mapped into a picture using the Hilbert curve.

Code to generate the image would map from 2D to 1D to find the color of each pixel, and the Hilbert curve is sometimes used because it keeps nearby IP addresses close to each other in the picture.

[5] The locality property of the Hilbert curve has also been used to design algorithms for exploring regions with mobile robots[6][7] and indexing geospatial location data.

Code to do this would map from 1D to 2D, and the Hilbert curve is sometimes used because it does not create the distracting patterns that would be visible to the eye if the order were simply left to right across each row of pixels.

[11][12] The linear distance of any point along the curve can be converted to coordinates in n dimensions for a given n, and vice versa, using any of several standard mathematical techniques such as Skilling's method.

Common programs such as Blender and Cinema 4D use the Hilbert Curve to trace the objects, and render the scene.

[citation needed] The slicer software used to convert 3D models into toolpaths for a 3D printer typically has the Hilbert curve as an option for an infill pattern.