Animals for survival in complex, time-evolving environments can estimate in a "single parallel run" the fitness of different alternatives. Understanding of how the brain makes an effective compact internal representation (CIR) of such dynamic situations is a challenging problem. We propose an artificial neural network capable of creating CIRs of dynamic situations describing the behavior of a mobile agent in an environment with moving obstacles. The network exploits in a mental world model the principle of causality, which enables reduction of the time-dependent structure of real situations to compact static patterns. It is achieved through two concurrent processes. First, a wavefront representing the agent's virtual present interacts with mobile and immobile obstacles forming static effective obstacles in the network space. The dynamics of the corresponding neurons in the virtual past is frozen. Then the diffusion-like process relaxes the remaining neurons to a stable steady state, i.e., a CIR is given by a single point in the multidimensional phase space. Such CIRs can be unfolded into real space for execution of motor actions, which allows a flexible task-dependent path planning in realistic time-evolving environments. Besides, the proposed network can also work as a part of "autonomous thinking", i.e., some mental situations can be supplied for evaluation without direct motor execution. Finally we hypothesize the existence of a specific neuronal population responsible for detection of possible time-space coincidences of the animal and moving obstacles.