This is the same gut-microbiome bistability as the paired 3D landscape simulator, but computed by an entirely different, independent mechanism: instead of one order parameter rolling on a cusp-shaped potential, this version simulates the two competing bacterial guilds as spatial concentration fields u(x,y) (fiber-fermenters) and v(x,y) (protein-fermenters) spreading and fighting for territory across a 2D petri-dish grid, under classical competitive Lotka-Volterra kinetics with diffusion:
∂u/∂t = D∇²u + r₀·u·(1 − (u + α·v)/Kᵤ)
∂v/∂t = D∇²v + r₀·v·(1 − (v + β·u)/K_v)
Kᵤ = K·(1 + b·h), K_v = K·(1 − b·h) [h = diet bias]
α = β = 1 + k (competitive-exclusion slider)
Here D∇² is real 2D diffusion (a 5-point finite-difference Laplacian, computed every substep on a live grid), and the reaction term is the textbook two-species competition model: when α > 1 and β > 1 — each guild suppresses the other more than it self-limits — the system is provably bistable: two stable pure states (all-fiber or all-protein) separated by an unstable interior equilibrium, exactly the "alternative stable states" behavior seen in real gut ecosystems.
- Diet slider — sets h, which rescales each guild's effective carrying capacity Kᵤ/K_v (more dietary fiber literally means more substrate ceiling for the fiber-fermenter guild). Push it hard enough and one guild's ceiling collapses toward zero, forcing a diet-driven takeover even from a mixed starting community.
- Competitive exclusion k — sets α = β = 1+k. Above the k=0 (α=β=1) threshold the interior equilibrium becomes an unstable saddle and the two pure states become genuinely alternative — below it, in principle, a single stable mixed community would persist instead.
- Antibiotic pulse — independently randomizes the surviving fraction of u and v in every grid cell (a real antibiotic course doesn't kill both guilds by the same amount, or in the same place, every time). Because the post-pulse mixture is no longer at the resident guild's fixed point, the deterministic competition dynamics can carry the whole colony into the other guild's basin — this is why microbiome recovery after antibiotics is so often incomplete, not from leftover drug, but because the ecosystem resettled into a different equilibrium.
- Domain interface length — counts grid-cell boundaries where the locally dominant guild switches. A single, fully-resolved colony has an interface near zero; a patchy, contested colony (weak competition, high noise, or shortly after a pulse) has a long, actively moving interface — a direct, computed measure of how settled the ecosystem currently is.