Hilbert Curves are space filling curves with the provable best locality characteristics - for example, given a two-dimensional Hilbert curve, points that are close by on the plane will be close by on the curve as well.
This is an attempt to map the RGB color space onto a 2D plane using Hilbert curves so that the transitions between colors are as smooth as possible - that is, colors that are nearby in RGB space will be nearby picture.
Hamilton's paper on the subject is extremely illuminating, and was my primary source for an understanding of the ideas involved in higher-dimensional Hilbert curves, although there is a subtle bug that trips up implementation.
The Wikipedia page is also a good resource, and has a relatively easy-to-understand implementation of the coordinate transforms for the 2D curve.
This project was an attempt to traverse the entire RGB space through a Hilbert curve in 3 dimensions and then draw the result as a Hilbert Curve in 2 dimensions.
Last of all, a shout out to Aldo Cortesi, whose implementation I found after writing my own. Aldo also produces visualizations for alternative traverals of RGB space, wrapping them up in a nice helper program.
Further development will focus on documenting the code, trying to explain some of the math more intuitively, cleaning up the code, and comparing alternative traversals of RGB space. I also intend to implement a "sort" feature that takes a picture, maps its pixels to a Hilbert Curve in 3D, sorts the pixels by distance along the curve, and draws the result as a 2D Hilbert curve.
This picture was created by simply mapping every single color in RGB space to a point in the picture plane, no fancy traversals involved.
This picture was created by mapping a straight traversal of RGB space to a hilbert curve traversal of the picture plane.
