Triple-Alpha Process: Reaction-Rate & Energy-Ladder Diagram (2D)

This is the 2D-native counterpart to the 3D triple-alpha particle simulator. Rather than rendering individual α/⁸Be/¹²C spheres colliding in a box, it integrates the mean-field helium-burning rate equation dY/dt = -3k(T,ρ)Y³ directly — using its exact analytic (Bernoulli) solution every frame for unconditional numerical stability — and turns the result into three genuinely 2D instruments: a live He-4/C-12 concentration strip chart, a log-rate-vs-temperature diagnostic exposing the reaction's brutal T-sensitivity, and a real nuclear energy-level ladder (3-alpha threshold → ⁸Be+α → the 7.65 MeV Hoyle resonance → ¹²C ground state) that flashes once per real carbon nucleus the rate equation produces. Toggle the Hoyle resonance off to watch the log-rate curve go flat and the ladder go quiet — the same "~20× slower without it" fact the 3D model demonstrates, reached here through a completely different, chart-and-diagram mechanism.