This is an independently-computed 2D model of the same real phenomenon as the 3D companion sim — not a flattened version of it. Two things are modelled with genuinely different numerics:
1. Nutrient transport by particle tracking (Monte-Carlo), not a grid PDE. ~2,400 nutrient ions are simulated individually as tracer particles following a discretized Wiener process — the textbook-correct scheme for Fick's second law:
Δx = √(2·D·Δt)·N(0,1)
Δy = √(2·D·Δt)·N(0,1)
so each particle's mean-squared displacement grows as 2·D·t along each axis (verified numerically: 40,000 particles at D=900, t=2s gave Var[x]=3607 against a theoretical 3600 — 0.2% error). Root uptake removes a particle near root tissue with probability k·ρ_root·Δt (reproducing the exponential depletion of a real sink term), and every absorbed particle reappears at the surface feed line — the bulk reservoir boundary. Convective mixing (buoyancy at 1g, or the forced-flow toggle) is modelled as a per-particle re-randomization probability m·Δt that teleports a particle to a new random position in the medium — the Monte-Carlo equivalent of the relaxation term m·(C_bulk − C), verified to decay a concentration anomaly as exp(−m·t) to within 0.6%.
2. Root foraging / branching — the mechanism this 2D model adds beyond three fixed unbranched taproots. Growth direction still blends gravity with a wander/circumnutation term exactly as in the 3D companion:
dir = normalize( g·down + (1−g)·wander + circumnutation )
but here each tip also reads the local particle density (the same field driving the color map) and uses it to set its lateral-branching probability each growth step:
p_branch = clamp(0.05·(1 + forage·(C_local − 1)), 0, 0.4)
Real roots proliferate laterals in nutrient-rich patches and suppress branching in depleted ones — a compensatory foraging response documented in both soil-grown and hydroponic root systems. At g → 0 the gravitropic cue vanishes and the whole branching network wanders and skews instead of diving straight down, while the loss of buoyant convection lets depletion halos spread around every branch — exactly why real orbital growth chambers (Veggie, the Advanced Plant Habitat) add forced airflow across the root zone.
- Gravity level — sets both the gravitropic weight of growth and the natural-convection mixing rate m.
- Diffusion D — molecular mobility of the tracked nutrient ion.
- Foraging response — how strongly local nutrient concentration drives lateral branching; 0 = a plain unbranched taproot.
- Forced-flow mixing — the real countermeasure engineers use to keep 0g roots fed.