Step 0Active hyphae –Length – mDissipation P –Robustness –

Drag to orbit, wheel or pinch to zoom. Click a tree (or use the buttons) to cycle it: sunlit source (+), shaded sink (–), neutral. Glowing tubes are fungal hyphae under the moss (thicker = more conductance, drawn much larger than real); yellow dots are carbon moving in the direction of flow.

Mycorrhizal Network Under a Forest Floor: Adaptive Hyphae, Flux Feedback and Source-Sink Flow Lab

A fungal network under a forest floor starts as a uniform mesh. Flow strengthens the hyphae that carry it and starves the rest, so a transport network grows between sunlit and shaded trees.

Trees (source / sink / neutral)

Network rule

View and speed

Live readouts

Network over time (relative to the start)

Experiment: how does γ shape the network?

Regrows the mesh for 700 steps at eight values of γ with your current trees, turnover and flux. Cost (active length) and robustness fall as γ rises, while the transport effort P rises.

Independent numerical checks

Controls

Drag or one finger: orbit; wheel or pinch: zoom. Click a tree or press its button to change its role. Growth speed is solver steps per frame.
You need at least one source and one sink for anything to flow. Presets set trees, γ and μ and restart the mesh. Quality High is the default; Low (or ?q=low) shrinks shadows and pixel ratio.

The science

Model. The soil is a graph of 64 junctions and 210 possible hyphae of length L_ij and conductance D_ij (a stand-in for tube cross-section). Carbon moves like current in a resistor network, with a source s_i at sunlit trees and an equal total sink at shaded ones.

Flow (Kirchhoff). Σ_j (D_ij/L_ij)(p_i - p_j) = s_i, flux Q_ij = (D_ij/L_ij)(p_i - p_j). Solved with preconditioned conjugate gradients.
Adaptation (Tero-type). dD/dt = |Q|^γ - μ D: hyphae that carry flux thicken, unused ones decay with turnover rate μ. This is the rule behind the slime-mould network experiments of Tero and colleagues, used here as a model of how adaptive transport networks can self-organise.
What γ does. γ = 1 converges to the cheapest route for one source and one sink (the page checks this on a two-route graph). γ < 1 keeps parallel routes (a robust mesh); γ > 1 concentrates flow on a few trunks (a sparse tree). The sweep measures it.
Effort. P = Σ L Q²/D = Σ s_i p_i is the dissipation (checked); a sparser network pays more P but less hypha volume Σ L D.
Robustness. The share of active hyphae that are not bridges: removing a bridge cuts some sink off from every source (breadth-first search).

Honest simplifications. This is a phenomenological network model. Real mycorrhizal networks are built by growing and branching tips, differ by fungal species, and the amount of carbon that trees really exchange through them is an active research question: this page shows how a flux-feedback rule shapes a network, not what a particular forest does. The flux units are dimensionless, the graph is a jittered lattice rather than measured hyphae, hyphae are drawn far thicker than the micrometre-scale reality, and mushrooms only mark where the network is dense. The thresholds (active = 5 % of the thickest hypha) are display choices.

Terrain, trees and mushrooms were modelled and baked in Blender and rendered with Three.js. Independent educational model.

FPS – · – triangles ·