This is a 2D-native counterpart of the Mycelium Composite Growth Lab: instead of tinting discrete voxels in BFS-distance order from spore seeds, the colonized fraction P is a continuous scalar field P(x,y,t) on a top-down grid of the substrate sheet, evolved with the Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher-KPP) reaction-diffusion equation — the textbook model for a front of a self-replicating population invading empty territory:
∂P/∂t = r(T,H)·P·(1−P) + D(fiber)·∇²P
r(T,H) = r_max · exp(−(T − T_opt)² / (2σ²)) · clamp((H − 50) / 30, 0, 1)
D(fiber) = D₀ · (0.6 + 0.008·fiber%) [coarser hemp hurd ⇒ larger
interstitial gaps ⇒ faster
hyphal-tip spread]
The reaction term is the same logistic hyphal-growth kinetics as the 3D lab; the new Laplacian term is what makes this genuinely spatial: it lets the colonized region grow outward from each spore point as a real propagating front, at the classic Fisher-KPP minimum wave speed v ≈ 2·√(r·D), rather than by re-ordering a static distance field. The grid is solved explicitly (5-point Laplacian stencil, zero-flux/Neumann edges, sub-stepped for numerical stability) and every frame's mean colonized fraction P̄ feeds the same bulk-property formulas as the 3D lab:
ρ(P̄) = ρ_sub·(1−P̄) + ρ_bound(fiber)·P̄ [bulk density]
σ(P̄) = σ_max(fiber) · P̄^2.2 [compressive strength,
percolation-like exponent]
Fiber content still trades density for strength the same way (more hemp hurd ⇒ lighter but tougher composite), and the avoided-CO₂ estimate uses the same illustrative cradle-to-gate factors (~3.5 kg CO₂e/kg virgin EPS vs. ~0.5 kg CO₂e/kg mycelium composite) applied to the block's current mass.
- Temperature / Humidity — set r(T,H), the local reaction (colonization) rate.
- Fiber content — sets both the diffusion coefficient D and the final density/strength trade-off.
- Pause / Reseed batch — freeze the clock, or start a fresh sheet with new random spore points.