Really Impressive. I wonder if you could use this to visualize a neural net that's solving actual problems.
However, you might be able to make some cool visualizations if your ANN was a Spiking Neural Network.
Would it be useful though? Maybe. Probably not as the fact that a neuron fires isn't nearly as useful as why it fired (what it represents).
But I like that you mention time. It always seemed odd that NN's today completely ignore that aspect. Sure whether a neuron fires is binary. But the accumulation of spikes is not binary and highly temporal. yet we completely ignore this aspect.
In a machine learning neural network there is no integration; they are basically just nonlinear data transformations that can (usually...) be trained.