Seamless Patterns

One nice property of digital marbling is that the patterns can be made seamless. In other words, you can place copies on each side of a pattern, and the images will match up. In this manner, you can create images of any size without having to compute huge numbers of pixels, which consumes more computation time; doubling the resolution of the image increases the computation time by a factor of four, since there are four times as many pixels.

Technically, this is called “tessellating the plane”. You have to ensure that the pattern continues across the top and bottom edges and across the left and right edges, as if the pattern was mapped onto the surface of a torus.

At the moment, I can’t make patterns that contain circles and vortices seamless. I do believe it’s possible, but I just haven’t been able to figure it out yet.

Here is an example. On the left is a variant of the Bird Wing, and the image on the right is made up of four copies of it. The left-hand image was originally computed with 3,600 pixels horizontal resolution, which is enough for an A4 sheet of paper. The original image on the right had a horizontal resolution of 7,200 pixels, which is enough for A2. (Like all images on this website, the resolution has been reduced significantly from the original, so that the pages load faster in the web-browser.)