The Sznajd model ("United we stand, divided we fall") simulates opinion dynamics on a lattice. Pairs of agreeing neighbors persuade their neighbors; disagreeing pairs have no influence. Watch consensus emerge.
Parameters
Grid size L30
Initial +1 frac0.50
Speed5
Anti-conformist %0.00
Statistics
Steps: 0
+1 fraction: -
Magnetization: -
Status: -
Theory
1D: consensus always
reached in finite time
2D: consensus ~L² steps
or frozen domain walls
Critical p=0.5: bifurcation
at perfect balance
Ferromagnet analogy: T=0
Ising dynamics
Rule: Select pair (i, i+1). If sᵢ = sᵢ₊₁ (agree), set sᵢ₋₁ = sᵢ₊₂ = sᵢ. In 2D, if a 2×1 plaquette agrees, all 4 outer neighbors adopt their opinion. Key result: With probability p of initial +1, the system reaches +1 consensus with probability p (linear!). In 1D this is exact; in 2D frozen domain walls can appear for p≈0.5. Adding anti-conformists (who do opposite) can stabilize minority opinions — a model of contrarians in social systems.