Tokunaga branching was proposed in 1978 as a self-similar branching structure for drainage networks. It is a much more robust constraint on alternative models than Horton-Strahler fractal scaling. Tokunaga branching was independently developed for diffusion-limited aggregation (DLA) clusters some 15 years later. This scaling is also applicable to aftershock sequences. Models and natural hazards that exhibit self-organized criticality have received wide attention. The forest-fire model is relatively simple and is now well understood. The dominant process is the coalescence of growing clusters of model trees. It has been shown that this coalescence is also a Tokunaga branching process.