The Voronoi Diagram is a geometrical structure that is widely used in scientific or technological applications where proximity is a relevant aspect to consider, and it also resembles natural phenomena such as cellular banks, rock formations or bee hives, among others. Typically, computing the Voronoi Diagram is done in a static context, that is, the location of the input seeds is defined once and does not change. In this work we study the dynamic case where seeds move, which leads to a dynamic Voronoi Diagram that changes over time. In particular, we consider uniform random moving seeds, for which we propose the dynamic Jump Flooding Algorithm (dJFA), a variant of JFA that uses less iterations than the standard JFA. An experimental evaluation shows that dJFA achieves a speedup of up to 5.3 x over JFA, while maintaining a similarity of at least 88 % and close to 100% in many cases. These results contribute with a step towards the achievement of real-time GPU-based computation of dynamic Voronoi diagrams for any particle simulation.