Agents interact only if |x_i - x_j| < ε. Each interaction moves opinions toward each other by factor μ. Clusters emerge from continuous opinion space [0,1].
Deffuant et al. (2000) bounded confidence model:
x_i(t+1) = x_i(t) + μ(x_j - x_i) if |x_i-x_j| < ε
x_j(t+1) = x_j(t) + μ(x_i - x_j)
Phase transition at ε_c ≈ 0.5 (consensus vs. polarization). Number of clusters ≈ 1/(2ε). Heterogeneous ε or extremists can prevent consensus even at large ε.
Left: opinion trajectories over time. Right: opinion distribution histogram.