At the coarsest level of description, neurons are non-linear oscillators that when coupled together in tissue through excitatory and inhibitory connections give rise to complex spatio-temporal patterns. When organized, these patterns are capable of processing and storing sensory information, and actuating musculature. Extrapolating from this general definition of a neuronal network, we demonstrate that these dynamics can be captured on an abiologic reaction--diffusion platform by exploiting advances in soft lithography that allow the engineering of synthetic reaction-diffusion networks. We employ the well-known oscillatory Belousov-Zhabotinsky reaction and develop methods to create diffusively coupled networks involving hundreds of nodes over which we design (i) the topology of the network, the (ii) boundary and (iii) initial conditions, (iv) the volume of each reactor, (v) the coupling strength, and (vi) whether the coupling is of an inhibitory or excitatory nature. Additionally, using a light sensitive catalyst and a digital projector, we can dynamically change the topology of the network by reversibly pruning nodes from the network. See http://fradenlab.com and T. Litschel, M. M. Norton, V. Tserunyan and S. Fraden, "Engineering reaction--diffusion networks with properties of neural tissue," Lab on a Chip 18, 714 - 722, (2018).