Hornet Invasion

Chapter 7 of The Nature of Code, Cellular Automata, generates global spatial pattern from local neighbor rules on a grid. Biological range expansion is a spatial spread process that a cellular automaton can approximate.

GBIF already maps the yellow-legged hornet’s spread year by year; I stamp those points onto a grid and let a local rule fill the gaps between surveys.

The page loads GBIF occurrence records for Vespa velutina, the yellow-legged hornet, across Europe by year from 2013 to 2025. Each year’s coordinates are stamped onto the grid as live cells, and a probabilistic neighbor rule fills the intervals between recorded years. The automaton’s growth is calibrated to the observed occurrences, so the advancing front approximates the documented invasion.

A cellular automaton updates each cell from its neighborhood, \(s_{i,j}^{\,t+1} = f\!\left(\{s_{i',j'}^{\,t}\}\right)\), here over the 8-cell Moore neighborhood \(\lvert i'-i \rvert \le 1,\ \lvert j'-j \rvert \le 1\). Colonization is probabilistic and linear in neighbor count: an empty cell with \(k\) occupied neighbors becomes occupied with probability \(P = \min(1,\, c\,k)\) for a small constant \(c\) (here \(c = 0.04\)). Recorded occurrence counts rise roughly geometrically year over year, the signature of an expanding invasion front.

Data source: GBIF Occurrence API
Endpoint: https://api.gbif.org/v1/occurrence/search?scientificName=Vespa%20velutina&year=YYYY&hasCoordinate=true
Access: Public, no key. Loaded from an hourly server-side refresh when possible, with a bundled snapshot fallback, and a live browser fetch only when the API allows CORS. Data window: Jan 1, 2013 - Dec 31, 2025 (pulled Aug 6, 2026 UTC)