Poisson Process — Timeline, Staircase & Gap Histogram

This simulator runs a genuine continuous-time Poisson counting process across three linked panels: a scrolling timeline of event arrivals (drag it to scrub back through history), a live staircase tracing the counting function N(t), and a running histogram of the exponentially-distributed interarrival gaps compared against the theoretical curve λ·e^(-λx). 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.