Dynamically reconfigurable platforms based on network-on-chips (NoC) could be a viable option for the deployment of large heterogeneous multicore designs. The dynamic nature of these platforms will mean that run-time application mapping and core management will represent a key challenge since the exact tasks requirements and workloads will not be known a priori. Considering the Manhattan distance among tasks as a measure of efficiency for a mapped application, this study proposes a distributed stochastic dynamic task mapping strategy for mapping applications efficiently onto a large dynamically reconfigurable NoC. The effectiveness of the mapping scheme is investigated considering the transient and steady states of the dynamic platform. The comparison with state-of-the-art centralised dynamic task mapping methods shows more than 26.4% improvement in application communication distance during steady state, which implies lower energy consumption and lower execution time.