The Wolfram Physics Project posits the existence of abstract relations between atoms of space whose pattern defines the structure of physical space. In this approach, two branches of evolution at a particular time are "adjacent" if they share an immediate ancestor in their multiway graph. Tracing through the connections of such graphs, termed branchial graphs, then leads to the notation of branchial space.
While causal graphs provide a summary of the evolution of a system based on capturing the causal relationships between events, branchial graphs provide a different kind of summary based on capturing relationships between states on different branches of a multiway system. Branchial graphs capture relationships between states on different branches at a given step and so define a map for exploring branchial space in a multiway system (Wolfram).
