Watch It Fire
Here's the function you just drilled, running live. This time the input isn't constant — it's a wobbling sine wave, so the neuron fires in bursts. Same three-panel view electrophysiologists use.
This is the LIF neuron solved by Euler's method — the same "V[k+1] = V[k] + Δt·dV" step, run 1000 times. The input now wobbles as a sine wave, so the neuron fires in bursts when the input rides high and falls silent when it dips.
Slide the input strength and watch the raster. When the wavy input rides high, the bucket fills past threshold and the neuron spikes rapidly; when it dips, the neuron goes quiet. This is Euler's method doing real neuroscience — no exact formula required.
Why this matters: with a constant input the LIF has an exact solution (last quest), but with a time-varying input like this one, it usually doesn't. Euler doesn't care — it just steps. That's the whole point of numerical methods: they work when the math gets too hard to solve by hand.