Poisson Process — Live Event Arrivals

This simulator runs a genuine continuous-time Poisson counting process: events arrive one at a time with exponentially-distributed gaps, and every accepted arrival is drawn as a marker sliding along a scrolling timeline while a live staircase traces the counting function N(t) above it. Switch to time-varying mode to watch the same process driven by a sinusoidal rate λ(t), sampled correctly with the thinning (Lewis–Shedler) rejection algorithm rather than a fixed-interval approximation, and compare the live estimated rate λ̂ = N(t)/t against the target λ as it converges.