Bak-Sneppen Model
Interactive 3D visualization of the Bak-Sneppen model of self-organized criticality.
About this notebook
The Bak-Sneppen model is a simple model of biological co-evolution and a classic example of self-organized criticality. Species sit on a ring, each with a random fitness between 0 and 1. Each step finds the species with the lowest fitness and replaces its fitness, and that of its two neighbors, with new random values.
This notebook runs the model interactively. Sliders set the number of species and the number of steps per click, and the Simulate button advances the evolution. marimo's state keeps the fitness values between clicks, so the simulation continues where it stopped.
A 3D stem plot shows the fitness of every species on the ring, with camera sliders to rotate and tilt the view. After enough steps, almost all fitness values collect above a threshold near 0.667. The rules do not contain this threshold. It emerges from the dynamics.
