Nowadays, one of the main challenges in computer architectures is scalability; indeed, novel processor architectures can include thousands of processing elements on a single chip and using them efficiently remains a big issue. An interesting source of inspiration for handling scalability is the mammalian brain and different works on neuromorphic computation have attempted to address this question. The Self-configurable 3D Cellular Adaptive Platform (SCALP) has been designed with the goal of prototyping such types of systems and has led to the proposal of the Cellular Self-Organizing Maps (CSOM) algorithm. In this paper, we present a hardware architecture for CSOM in the form of interconnected neural units with the specific property of supporting an asynchronous deployment on a multi-FPGA 3D array. The Asynchronous CSOM (ACSOM) algorithm exploits the underlying Network-on-Chip structure to be provided by SCALP in order to overcome the multi-path propagation issue presented by a straightforward CSOM implementation. We explore its behaviour under different map topologies and scalar representations. The results suggest that a larger network size with low precision coding obtains an optimal ratio between algorithm accuracy and FPGA resources.