We present a computationally simple yet efficient method for planning global trajectories in deterministic dynamic environments of arbitrary dimensions and complexity. The method leverages morphological operations on a discrete Minkowski spacetime and constructs cognitive maps that encode the earliest arrival time at each point. We established a solid theoretical foundation, ensuring the approach's applicability in risk-critical missions. The method is illustrated using simulations of terrestrial robots and flying drones, resulting in efficient yet conservative solutions that closely mimic the behavior of biological agents.