Same population model as the 3D vesicle simulator, rendered as a genuine 2D packed-circle scene plus a live strip chart — not a flattened camera view. Each protocell is a lipid vesicle with membrane area A and encapsulated content C, both growing under Monod-style nutrient limitation f(N)=N/(N+K):
dA/dt = k_A · f(N)
dC/dt = k_C · f(N)
V → C / c₀ (volume relaxes toward the osmotic target)
A sphere of volume V has the minimum possible area Amin=4π(3V/4π)^(2/3). The reduced excess area ν = A/Amin tracks how much membrane a vesicle carries beyond that geometric floor; fission fires once ν crosses the threshold νc, splitting content and area with binomial-like noise between two daughters.
ν = A / A_min(V), ν ≥ 1 (physical floor)
fission when ν ≥ ν_c
Fix applied here vs. the 3D source: the 3D engine computes ν = A/A_min(V) directly from the relaxing volume without ever clamping it, and because volume lags area during the very first growth steps it can numerically dip to ν≈0.6 — physically impossible, since a sphere is by definition the minimum-area shape for a given volume, so real ν can never go below 1. This 2D engine clamps nu = Math.max(1, area / aMin), matching the invariant the theory text itself states.
- kA / kC — membrane vs. content synthesis rates; a bigger kA/kC ratio pushes ν up faster and divides sooner.
- νc — the shape-instability ratio that triggers fission into two daughters.
- Nutrient consumption efficiency — how much of the shared nutrient pool each unit of synthesis burns; higher values exhaust the pool (and stall growth) before ν can climb far, so cranking this down is what lets a population actually reach several fission rounds.
- Population cap — a hard ceiling on simulated protocells (canvas/perf limit); growth pauses once reached.
- Drag the main view to pan, scroll to zoom; the strip chart below tracks population, nutrient % and mean ν over time.
This is the same excess-area-driven division mechanism proposed for early protocells (Zhu & Szostak-style vesicle models): membrane growth outpacing osmotic volume growth is, on its own, enough to make a minimal cell divide — no genetic division machinery required.