Devlog #65 – Wave 45: Galactic Rotation Curve, Herd Immunity & Population Genetics

Release Stats

New Simulations

Technical Highlights

🌌 Galactic Rotation Curve: NFW Halo Physics

The rotation curve simulation uses two canvases side by side. The left canvas animates 170 stars (140 spiral arm + 30 bulge) with each star's angular velocity derived from v(r)/r where v(r) is the total circular velocity at radius r. Stars are coloured blue-to-yellow-to-red based on their speed — fast inner stars appear warm, slow outer stars appear cool — which counter-intuitively inverts in the dark matter case (outer stars stay fast).

The right canvas plots four curves simultaneously: the Keplerian prediction for disk-only mass (V ∝ 1/√r, red dashed), the visible disk contribution (yellow semi-transparent), the NFW halo contribution (blue semi-transparent), and the total observed curve (bright cyan, 2.5px). The NFW halo velocity is derived from the enclosed mass integral: M_enc(r) ∝ [ln(1+r/rs) − (r/rs)/(1+r/rs)], which gives a nearly flat rotation curve at large r. The dark matter fraction slider continuously updates all four curves in real time.

💉 Herd Immunity: SIRV ODE Architecture

The epidemic model uses a compartmental ODE system with four states: susceptible (S), infected (I), recovered (R), and vaccinated (V). Vaccination is applied as a fixed initial condition — a fraction vacPct/100 of the population starts immune — rather than a continuous rate. This represents a pre-campaign vaccination scenario.

The ODE is integrated with forward Euler at dt = 0.3 days, running 3 steps per animation frame for a ~6× real-time speedup. The transmission rate uses β = R₀ / infDays and recovery rate γ = 1/infDays, giving an effective R₀ consistent with the slider. The 30×30 population grid is re-synchronised each frame by sorting cells into S/I/R/V order proportional to the ODE fractions — a pragmatic approach that keeps the visual consistent without running a full agent model.

The herd immunity threshold indicator (p_c = 1 − 1/R₀) updates immediately when any control changes, before even running the epidemic. This allows students to understand the threshold conceptually before pressing "Run".

🧬 Population Genetics: Hardy-Weinberg & Drift

The simulation runs a Wright-Fisher–style discrete generation model. Each generation, allele frequencies are updated by three mechanisms in sequence: (1) selection — genotype fitness weights (wAA, wAa, waa) renormalise the allele frequency; (2) mutation — A→a at rate μ and a→A at rate μ/10; (3) genetic drift — binomial sampling of N diploid individuals from the updated allele frequency.

The dot grid shows up to 400 individuals, coloured by genotype: purple = AA, indigo = Aa, dark grey = aa. The frequency chart plots p(A) in solid purple and q(a) = 1 − p(A) in dashed indigo, over up to 500 generations. The Hardy-Weinberg expected frequencies (p², 2pq, q²) are displayed in the stat bar, making it easy to spot deviations due to drift or selection.

The sickle-cell preset enables heterozygote advantage mode (HETERO_ADV = true), where wAa > wAA > waa — modelling balancing selection that maintains both alleles at an intermediate equilibrium frequency even under strong selection pressure. This is one of the best-known examples of natural selection maintaining genetic diversity.

What's Next

The category coverage continues to improve — immunology (now 2 sims), astrophysics (now 4 sims). High-priority targets for Wave 46 include enzyme kinetics (Michaelis-Menten saturation curves), quantum chromodynamics (colour confinement visualiser), and tectonic plates (mantle convection & plate boundaries). The blog series is also due for a Spotlight #48 and Learning #36 in the coming weeks.