Einstein Coefficients 2D: Spontaneous vs Stimulated Emission

This 2D simulator models the same real ensemble of two-level atoms as the 3D version, driven by the same A and B Einstein coefficients that make Planck's law self-consistent, but lays it out across three linked panels: a pannable/zoomable 2D atom cloud where each dot flips colour on every transition and fires a small photon spark, a live energy-level diagram whose four arrows (absorption, pump, stimulated and spontaneous emission) thicken and animate in proportion to their real-time rates, and a strip chart tracing the excited-state fraction over the last 20 seconds. Turn up the temperature and the excited-state population climbs but always stays a minority — turn on the external pump instead and watch the ensemble cross the population-inversion threshold that every real laser depends on.