Quantum Zeno Effect — Survival Curve & Trial Statistics (2D)

This is an independent 2D companion to the 3D quantum Zeno effect simulator, built around a genuinely different visualisation mechanic rather than a flattened Bloch sphere: a bank of 180 independent Monte-Carlo trial atoms laid out on a 2D grid, each repeatedly attempting to survive N consecutive projective measurements spaced τ = T/N apart without ever collapsing into the excited state. Every gap it clears without collapsing keeps a trial alive; the instant one fails, it flashes red and restarts; the instant it strings together a full run of N clean gaps, it flashes green as a completed successful trial and restarts. Tallying successes against failures across all 180 atoms continuously builds a running empirical estimate of the survival probability, which a companion chart plots directly against the closed-form curve P_survive(N) = [cos²(π/2N)]^N sampled across N from 1 to 256 on a log axis — with the current N marked and the empirical value dropped onto it as a diamond that visibly converges onto the curve as more trials accumulate. A second scrolling oscilloscope trace follows one representative qubit's own P₁(t) with tick marks at every individual measurement event, so the same collapses being tallied in bulk on the grid can also be watched one at a time. Together the three views prove numerically, live, that packing more measurements into the same window drives the empirical survival fraction toward the theoretical prediction and toward 1 — the quantum Zeno effect, first confirmed experimentally with trapped ions by Itano et al. in 1990.