The branches of a tree can be viewed as redundant organs: they have the same functional roles and the same unlimited developmental potential. The most prominent aspect of tree form, here considered as an example of dynamic self-organization, is the relations among these branches. A branch is a source of information about its size, state and environment. A response to this information is the oriented vascular differentiation which connects the branch with the rest of the plant. A known phytohormone, auxin, is formed by shoot tissues and replaces this orienting influence of a shoot. This accounts for neighboring branches having specific, even competing, effects without any other branch specificity. The same phytohormone also elicits different processes throughout the plant, integrating their occurrence without recourse to a central control. Self-organization requires a positive feedback that enhances the development of a successful branch, and an inhibitory influence that reduces similar branch growth. Both roles could depend on the oriented vascular differentiation that is specified by auxin. Actual tree form at any given time is a transient dynamic state. One reason for this is that competition between branches is a long-term, gradual process. A second reason is that a periodic surfeit of root supplies enhances a seasonal formation of many branches which 'search' environmental possibilities, and most of these branches decline only gradually. The various aspects of tree form could thus depend on remarkably simple and robust principles, requiring only limited genetic information. Much of the necessary information about the details of tree form is generated by a Darwinian-like process of developmental selection, reaching a predictable overall outcome without following any strict plan. It is a case of self-organization in which the component structures, the tree branches, do not move, but do undergo long term developmental changes.