An agent-based model of the game in Funes, Orme and Bonabeau (Artificial Life IX, 2004) and Bonabeau, Funes and Orme ("Exploratory Design of Swarms", 2003). Each player picks two others, A and B, and follows one of two rules: move so that B is between A and you (Rule 1), or move so that you are between A and B (Rule 2). The sandbox lets you set the ratio of rules and the full relationship graph; the evolution tab breeds graphs from the playgrounds you select.
Positions update as Ai ← Ai + σeiθ with σ = δ = 2r per step, where r is an agent's radius. σ is cut back when the step would run into a wall or another agent. Rule 1 (keep B between A and me) follows the regions of Figure 1(a): coming from A's side of B the agent heads for the point u beside B, from the far side for v; once close to B it travels around B's edge to w, the point just past B on the line from A through B; anywhere farther along that line it moves straight onto the line and stops, because there the rule is satisfied. Rule 2 moves toward the closest point on the segment from A to B. Noise follows Figure 7: a random vector drawn in a square of side νδ is added to the intended step and the sum is renormalized.
rule A B with 1-based indices.Nine games run side by side, each with its own relationship graph. Click the playgrounds whose collective patterns you find most interesting (click again to deselect), then press "Breed next generation". Selected games are kept unchanged and the other slots are refilled from them. Repeat until something striking appears, then send that playground to the sandbox to read off its rules and study it at full size.
With one game selected, the procedure is the paper's: the other eight are rebuilt from it, four by mutation and four by recombination. With two or more selected, each new game is a crossover of two selected parents drawn at random, and its label names them (for example "3 × 7"). Crossover works across games, while the paper's recombination works between agents inside one game; both use the fact that agent i means the same player in every game, so A and B indices stay valid. Depending on the setting, some or all crossover offspring then receive the mutation operator.
Mutation (section 3.2) changes up to a chosen fraction of agents; for each one, A, B or the rule is redrawn at random with probability 1/3 each. Recombination copies one, two or three features from a random source agent into a target agent, again for up to that fraction of agents. If you tick "inject a random game", one of the eight offspring is replaced by a fresh random graph each generation to maintain diversity, as the paper describes.