Cortical plasticity is one of the main features that enable our capability to learn and adapt in our environment. Indeed, the cerebral cortex has the ability to self-organize itself through two distinct forms of plasticity: the structural plasticity that creates (sprouting) or cuts (pruning) synaptic connections between neurons, and the synaptic plasticity that modifies the synaptic connections strength. These mechanisms are very likely at the basis of an extremely interesting characteristic of the human brain development: the multimodal association. [...] To model such a behavior, Edelman and Damasio proposed respectively the Reentry and the Convergence Divergence Zone frameworks where bi-directional neural communications can lead to both multimodal fusion (convergence) and inter-modal activation (divergence). [...] In this paper, we build a brain-inspired neural system based on the Reentry principles, using Self-Organizing Maps and Hebbian-like learning. We propose and compare different computational methods for unsupervised learning and inference, then quantify the gain of both convergence and divergence mechanisms in a multimodal classification task. The divergence mechanism is used to label one modality based on the other, while the convergence mechanism is used to improve the overall accuracy of the system. We perform our experiments on a constructed written/spoken digits database and a DVS/EMG hand gestures database. Finally, we implement our system on the Iterative Grid, a cellular neuromorphic architecture that enables distributed computing with local connectivity. We show the gain of the so-called hardware plasticity induced by our model, where the system's topology is not fixed by the user but learned along the system's experience through self-organization.