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The mechanisms behind memory have been studied mainly in artificial neural networks. Several mechanisms have been proposed, but it remains unclear yet if and how these findings can be translated to biological networks. Here we unravel part of the mechanism by showing that cultured neuronal networks develop an activity connectivity balance. External inputs disturb this balance and induce connectivity changes. The new connectivity is no longer disrupted by reapplication of the input, indicating that a network memorizes the input, analog to attractor memory networks as demonstrated in Hopfield network models. A different input again induces connectivity changes upon first application but not after repeated stimulation. Returning to the first input no longer affects connectivity, showing that memory traces are stored in parallel. A simple computer model robustly reproduces the experimental results and shows that spike timing dependent plasticity suffices to store memory traces of different inputs in parallel in neuronal networks.