Stochastic computing was extensively studied for artificial neural networks (ANN) implementation with a good time/area trade-off on up-to-date FPGAs. We propose here to use the same paradigm for the hardware implementation of dynamic neural fields (DNF) on FPGAs. The all-to-all connectivity of these neural population models make straightforward hardware mappings impossible for high density fields. It is necessary to adapt the architecture to fit the cellular nature of computing substrates such as FPGAs. Following the previous work on randomly spiking dynamic neural fields, we propose here a new implementation inspired by stochastic ANNs. We introduce here the Cellular Array of Stochastic Asynchronous Spiking DNF model, or CASAS-DNF. While keeping the fully decentralized cellular characteristics, this new approach is much more competitive in terms of speed and area. We also show that the basic behaviors of DNFs are preserved. The low hardware cost and the cellular design of this model make it easily scalable.