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David Hilbert

David Hilbert was a German Mathematician who lived from the late 19th to mid 20th centuries C.E. Known mainly as a geometer, Hilbert also made significant contributions to set theory and logic. In 1891, he formally described a space filling curve, which now bears his name.

This project, like the Sierpinski project, does not really use much math, just mathematical structures. This time, I took the source image, averaged over square pixels, then replaced the pixels with copies of the first four iterations of Hilbert's space filling curve. Again, I used a Floyd-Steinberg based algorithm to diffuse the error.

The great thing about this picture, which isn't readily apparent, is that the entire picture is one solid curve starting at the bottom left corning, going through a large, Hilbert curve-shaped, path, and ending at the bottom right corner. This picture was never displayed at a show, but it was a fun project.

I can provide higher resolution images on request. Here is a detail of the Hilbert curve showing a number of iterations: