In branching simulation, a novel approach to simulation presented in this paper, a multiplicity of plausible scenarios are concurrently developed and implemented. In conventional simulations of complex systems, there arise from time to time uncertainties as to which of two or more alternatives are more likely to be pursued by the system being simulated. Under these conditions the simulationist makes a judicious choice of one of these alternatives and embeds this choice in the simulation model. By contrast, in the branching approach, two or more of such alternatives (or branches) are included in the model and implemented for concurrent computer solution. The theoretical foundations for branching simulation as a computational process are in the domains of alternating Turing machines, molecular computing, and E-machines. Branching simulations constitute the development of diagrams of scenarios representing significant, alternative flows of events. Logical means for interpretation and investigation of the branching simulation and prediction are provided by the logical theories of possible worlds, which have been formalized by the construction of logical varieties. Under certain conditions, the branching approach can considerably enhance the efficiency of computer simulations and provide more complete insights into the interpretation of predictions based on simulations. As an example, the concepts developed in this paper have been applied to a simulation task that plays an important role in radiology - the noninvasive treatment of brain aneurysms.