Voter Model & Noisy Voter Dynamics (2D)

Model

Dynamics

Parameters

Lattice size (N) 60

Flip noise (p) 0.010

Initial blue fraction 0.50

Updates / frame 5

Live Readout

Blue fraction

50.0%

Interface density

0.0%

Largest cluster

Steps

Consensus?

Elapsed

0.0 s

How it works

Every update step, a random cell copies the opinion (blue/red) of one randomly chosen von-Neumann neighbour — an asynchronous process, so later picks within the same sweep already see updated values, exactly as in the analytic voter model. On a finite periodic lattice this process always drifts toward one-colour consensus: there is no stable mixed equilibrium, only a random walk toward absorption at 0% or 100% blue.

Switching to Noisy Voter gives each update a probability p of instead adopting a uniformly random opinion rather than copying a neighbour. Even a tiny p keeps reintroducing disagreement, so the blue fraction settles into a fluctuating steady state around 50% instead of freezing at consensus — you can watch the magnetisation chart stop converging and start oscillating as p rises.

Interface density — the fraction of neighbouring cell-pairs that disagree; it falls to 0 at consensus and stays high under strong noise.
Largest cluster — the biggest connected same-colour region, found by flood-fill; it grows toward N² as the system nears consensus.
Paint — click/drag on the lattice to set opinions by hand (left = blue, right = red) and perturb a run in progress.

Blue opinion Red opinion Blue fraction over time