Space colonization is a process for iteratively growing networks of organic branches based on the distribution of attractors to which the branches are attracted. Originally described (PDF) by Adam Runions and collaborators at the Algorithmic Botany group at the University of Calgary, this system can be used to simulate the growth of leaf venation patterns and tree-like structures, as well as many other vein-like systems like Gorgonian sea fans, circulatory systems, root systems, and more.
Check out the Github repository for a more in-depth explanation of the algorithm along with a comprehensive list of both creative and technical references on the topic.