Landis 1998: colonisation probability p versus critical threshold pc≈0.31 determines whether civilisation spans the galaxy or fragments into isolated clusters
⚠ Theoretical — Landis 1998 percolation model
Model Parameters
BFS from galactic centre. Each neighbour of a colonised cell is colonised with probability p (seeded PRNG). p_c ≈ 0.31 (Landis 1998; note: 3D-cubic site threshold, not 2D bond).
Colonisation probability p0.30
0 (none)p_c=0.311.0 (all)
Random seed42
1500999
p vs p_c indicator
0p_c=0.311
Largest cluster
—
% of grid cells
No. of clusters
—
distinct regions
Below p_c
Civilisation fragments — no galaxy-spanning cluster forms.
40 × 40 Galaxy Grid — BFS percolation from centre
ColonisedUnreachableEarth / origin
Model description
This tool implements the Landis (1998) percolation model of galactic colonisation. A 40×40 grid of stellar systems is initialised with Earth at the centre. BFS expands outward: for each colonised cell, each of its 4 neighbours (N/S/E/W) is colonised with probability p, independently. The process terminates when no further expansion is possible.
Landis (1998) cites a critical percolation threshold of pc ≈ 0.31, which he attributes to 2D bond percolation. Note: the actual threshold for 2D square-lattice bond percolation is exactly 0.5; the value 0.31 matches the 3D simple-cubic site percolation threshold. The Landis paper's model geometry is ambiguous; 0.31 is retained here as the historically cited value. The qualitative argument is unchanged: below threshold the colonised region is bounded; above it a spanning cluster forms. Landis argues this explains the Fermi Paradox: if p < pc for any one civilisation, the galaxy is never fully colonised regardless of how many civilisations exist.
Limitations
The 2D grid is a severe simplification. Real galaxies are 3D structures with inhomogeneous stellar densities, travel times, and varying habitability. The model also assumes a single origin, constant p, and no re-colonisation of abandoned systems. These simplifications make it a conceptual illustration, not a predictive model.
Citation
Landis, G. A. (1998). "The Fermi Paradox: An Approach Based on Percolation Theory." Journal of the British Interplanetary Society, 51, 163–166. NASA NTRS: 19940022867.