A scientific report from the Essentia Memoria game universe. Its measurements come from the game's simulation; its real-world values come from the published works it cites.

Scientific report

Where a forest stops burning: the game’s fire law measured against the percolation threshold

Happened: October 28, 2026 at 2:52 PM UTC · Published: October 28, 2026 at 2:52 PM UTC

We burned 440 simulated forests with the game’s own fire law. Half the fires crossed a forest at a tree density of 0.588; percolation theory puts the threshold of an endless square grid at 0.59274621. The world plants its forests at 0.62, just above it, yet 6 of the 8 fire strengths its weather makes never leave a record, because a tree catches from a burning neighbour only by chance.

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Transcript

News from the Essentia Memoria game universe. Where a forest stops burning: the game’s fire law measured against the percolation threshold. We burned 440 simulated forests with the game’s own fire law. Half the fires crossed a forest at a tree density of 0.588. Percolation theory puts the threshold of an endless square grid at 0.59274621. The world plants its forests at 0.62, just above it, yet 6 of the 8 fire strengths its weather makes never leave a record, because a tree catches from a burning neighbour only by chance. These are measurements of the game’s model, not of real forests. Real wildfires turn on wind, slope, fuel moisture and terrain, which this grid rule does not hold. The forests are 64 × 64 cells, so the measured threshold carries a finite-size error, and density was sampled every 0.01. The world’s planting density is a value in the game’s code, not a measurement of any real forest. This report was written from the world record by a fixed template. The full story and its source records are on essentiamemoria.com.

The question

Does the game’s fire law stop spreading at the tree density percolation theory predicts, and what does that mean for the world’s own fires?

Claims, and where each one comes from

Simulated forests burned for the threshold440
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, ignition=whole left edge, lightning=0 · runs 440 · seeds forestSeed(densityIndex, k), k < 40
Fires that crossed the forest at tree density 0.552 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.55, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(0, k)
Fires that crossed the forest at tree density 0.564 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.56, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(1, k)
Fires that crossed the forest at tree density 0.575 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.57, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(2, k)
Fires that crossed the forest at tree density 0.5811 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.58, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(3, k)
Fires that crossed the forest at tree density 0.5922 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.59, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(4, k)
Fires that crossed the forest at tree density 0.6021 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.6, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(5, k)
Fires that crossed the forest at tree density 0.6134 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.61, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(6, k)
Fires that crossed the forest at tree density 0.6235 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.62, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(7, k)
Fires that crossed the forest at tree density 0.6339 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.63, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(8, k)
Fires that crossed the forest at tree density 0.6440 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.64, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(9, k)
Fires that crossed the forest at tree density 0.6540 / 40
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/applications.ts · stepFire (via fireCrosses) · size=64×64, regrow=0, spread=1, density=0.65, ignition=whole left edge, lightning=0 · runs 40 · seeds forestSeed(10, k)
Density at which half the fires cross (measured in the game)0.588
Game simulation · Computed by src/lib/broadcast-programming/public-science.ts · halfCrossingDensity · size=64×64, regrow=0, spread=1, ignition=whole left edge, lightning=0, resolution=0.01 · runs 440 · seeds forestSeed(densityIndex, k), k < 40
Site percolation threshold of the square lattice (real-world mathematics)0.59274621
Real-world knowledge · Source [1] [3]
Measured and theoretical threshold agree within the grid step (0.01)✓ |0.588 − 0.593| = 0.005
Game simulation · Computed by src/lib/broadcast-programming/public-science.ts · firePercolationStory · resolution=0.01 · runs 440 · seeds forestSeed(densityIndex, k), k < 40
The fire rule is the self-organised forest-fire model, with a catch chance per burning neighbourDrossel & Schwabl 1992
Real-world knowledge · Source [2]
Tree density the world plants its forests at0.62
Game simulation · Set in code src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts · WORLD_FOREST_DENSITY
Strike strengths whose fires never leave a world record6 / 8
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts · processesFromWorld → startProcess → processOutcomeFact · size=48×48 · runs 160 · seeds worldSeed 50000 + k, k < 20
A faint strike in dry air (catch chance 0.450): fires recorded · mean share burned0 / 20 · —
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts · startProcess → processOutcomeFact · size=48×48, regrow=0.01, spread=0.45 · runs 20 · seeds worldSeed 50000 + k, k < 20
A noticeable strike in dry air (catch chance 0.600): fires recorded · mean share burned0 / 20 · —
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts · startProcess → processOutcomeFact · size=48×48, regrow=0.01, spread=0.6 · runs 20 · seeds worldSeed 50000 + k, k < 20
A strong strike in dry air (catch chance 0.750): fires recorded · mean share burned2 / 20 · 8%
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts · startProcess → processOutcomeFact · size=48×48, regrow=0.01, spread=0.75 · runs 20 · seeds worldSeed 50000 + k, k < 20
A overwhelming strike in dry air (catch chance 0.900): fires recorded · mean share burned15 / 20 · 43%
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts · startProcess → processOutcomeFact · size=48×48, regrow=0.01, spread=0.9 · runs 20 · seeds worldSeed 50000 + k, k < 20
A faint strike in damp air (catch chance 0.158): fires recorded · mean share burned0 / 20 · —
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts · startProcess → processOutcomeFact · size=48×48, regrow=0.01, spread=0.158 · runs 20 · seeds worldSeed 50000 + k, k < 20
A noticeable strike in damp air (catch chance 0.210): fires recorded · mean share burned0 / 20 · —
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts · startProcess → processOutcomeFact · size=48×48, regrow=0.01, spread=0.21 · runs 20 · seeds worldSeed 50000 + k, k < 20
A strong strike in damp air (catch chance 0.262): fires recorded · mean share burned0 / 20 · —
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts · startProcess → processOutcomeFact · size=48×48, regrow=0.01, spread=0.262 · runs 20 · seeds worldSeed 50000 + k, k < 20
A overwhelming strike in damp air (catch chance 0.315): fires recorded · mean share burned0 / 20 · —
Game simulation · Computed by src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts · startProcess → processOutcomeFact · size=48×48, regrow=0.01, spread=0.315 · runs 20 · seeds worldSeed 50000 + k, k < 20

References, checked at their registry

[1] Newman (2000). Efficient Monte Carlo Algorithm and High-Precision Results for Percolation. Physical Review Letters. doi:10.1103/PhysRevLett.85.4104
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 2:52 PM UTC · the registry holds “Efficient Monte Carlo Algorithm and High-Precision Results for Percolation” (2000)
[2] Drossel (1992). Self-organized critical forest-fire model. Physical Review Letters. doi:10.1103/PhysRevLett.69.1629
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 2:52 PM UTC · the registry holds “Self-organized critical forest-fire model” (1992)
[3] Broadbent (1957). Percolation processes: I. Crystals and mazes. Mathematical Proceedings of the Cambridge Philosophical Society. doi:10.1017/S0305004100032680
Verified: the work exists and matches · checked at Crossref on Oct 28, 2026, 2:52 PM UTC · the registry holds “Percolation processes: I. Crystals and mazes” (1957)

Review

Not peer reviewed. No human scientist has reviewed this report. Its template was written with an AI assistant (Claude); the numbers come from running the game’s code, and the checks above are listed so anyone can repeat them.

Each cited DOI was resolved, and its title, year and first author matched the claim.
Each number in the headline and summary is accounted for by a listed claim.
Each simulation number names the code, parameters and seeds that produced it.
Each real-world value names the published work it comes from.

Code version: c6a8103412a4

What the record does not say

These are measurements of the game’s model, not of real forests. Real wildfires turn on wind, slope, fuel moisture and terrain, which this grid rule does not hold. The forests are 64 × 64 cells, so the measured threshold carries a finite-size error, and density was sampled every 0.01. The world’s planting density is a value in the game’s code, not a measurement of any real forest.

How this was written

Measured on the server by running the game’s own fire law with fixed seeds, so the same code gives the same numbers. Every cited work was looked up at its DOI registry before publication, and its title, year and first author compared with what is claimed here. Every number in the headline and summary is one of the claims listed below.

Source records: code:src/lib/sim/sciences/mathematics/cellular-automata/applications.ts#stepFire · code:src/lib/sim/sciences/mathematics/cellular-automata/world-processes.ts#startProcess · doi:10.1103/PhysRevLett.85.4104 · doi:10.1103/PhysRevLett.69.1629 · doi:10.1017/S0305004100032680