Self-assembled networks of nanoparticles and nanowires have recently emerged as promising systems for brain-like computation. Here we focus on percolating networks of nanoparticles which exhibit brain-like dynamics. We use a combination of experiments and simulations to show that the brain-like network dynamics emerge from atomic-scale switching dynamics inside tunnel gaps that are distributed throughout the network. The atomic-scale dynamics emulate leaky integrate and fire (LIF) mechanisms in biological neurons leading to the generation of critical avalanches of signals.These avalanches are quantitatively the same as those observed in cortical tissue and are signatures of the correlations that are required for computation. We show that the avalanches are associated with dynamical restructuring of the networks which selftune to balanced states consistent with self-organised criticality. Our simulations allow visualisation of the network states and detailed mechanisms of signal propagation.

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