The 3D version of this simulator integrates the point-kinetics equations as a deterministic ODE (Runge-Kutta). This 2D counterpart solves the same physical reaction network with a completely different, independently computed method: Gillespie tau-leaping, a Monte Carlo algorithm that treats neutrons and delayed-neutron precursors as discrete, countable packets undergoing random birth/death events, not a smooth continuous quantity. Three reaction channels fire stochastically:
R1 N → N±1 rate a₁ = |(ρ−β)/Λ|·N (net prompt production or loss)
R2 N → N+1, C → C−1 rate a₂ = λ·C (precursor decay emits a neutron)
R3 C → C+1 rate a₃ = (β/Λ)·N (a fission seeds a new precursor)
Every animation frame is split into short leaps of length h; within each leap the number of times every channel fires is drawn from a Poisson distribution with mean aᵢ·h (Gaussian approximation for large means), then N and C are updated by the sampled integer counts. Sixteen independent realizations run in parallel purely for statistics — the bold dot-cloud and graph line track realization #1, the faint lines are the other fifteen.
Because population sizes are finite integers instead of a continuous mean, this model reproduces something the deterministic ODE structurally cannot: real shot noise in the neutron count, and a genuine, nonzero probability that a barely-supercritical or delayed-critical chain reaction randomly dies out (both N and C hit exactly zero) before it ever takes off — exactly the statistical hazard that makes reactor startup and subcritical-multiplication measurements a real branching-process problem in practice, not just an exponential curve. The "predicted period" readout still comes from the same closed-form inhour equation as the 3D version, shown here purely as the theoretical reference the stochastic realizations should average toward.
- Reactivity ρ — the step change in criticality, in dollars ($ = ρ/β). Positive = supercritical.
- Delayed fraction β — compare a U-235-like core (β ≈ 0.65%) against a Pu-239-like core (β ≈ 0.21%, dies or goes prompt with far less reactivity).
- Prompt generation time Λ — sets how fast the prompt-production channel R1 fires; short Λ means noisier, faster leaps.
- Precursor decay constant λ — pace of channel R2, the slow precursor-paced climb.
- Ensemble die-out — how many of the 16 independent realizations have gone fully extinct (N=0 and C=0, an absorbing state with no source term) — watch it rise near delayed-critical, where the deterministic model would predict indefinite steady power for every realization.