I saw an interesting algorithm for creating branching veiny patterns called the Space Colonization Algorithm. Of course, I had to apply it to halftoning. Basically, the veins grow in the direction of their nearest destination points. Once the vein is close enough to a destination point, that destination is removed from the list, and growth continues toward others. A halftoning effect can be obtained by changing that ‘close enough’ distance.
Above, the modified algorithm is run with the starting point at the center. Below, the starting point is at the top center.
In that case, the branches grew simultaneously. You can get more interesting patterns if they grow sequentially. The next image has two versions using that technique: the branches in the left image are not aligned to the image, but the right ones are.