Social Sorting Village (3D)

What is modelled

Two classic, deliberately simple models from the social sciences, run on a town of lots. Neither claims to predict a real city; each shows how a collective pattern can emerge from simple individual rules, which is why they are used in teaching.

1. Schelling's segregation model (1971)

• Households of two groups (blue and orange roofs) and some empty lots sit on a grid with wrap-around edges. A household is unhappy when the share of same-group households among its occupied neighbours (Moore neighbourhood of radius R) is below its tolerance tau.
• Each tick, a few randomly chosen unhappy households move to a random empty lot where they would be content.
• Segregation index S = mean over households of (same-group neighbours / occupied neighbours). For random mixing of equal groups S is about 0.5.
• Famous result: even a mild preference (tau around 1/3) drives S far above tau, because every move changes the neighbourhood of others (a feedback loop). Very low tolerance leaves the town mixed.

2. Bounded-confidence opinions (Deffuant et al., 2000)

• Every household has an opinion x between 0 and 1 (blue to orange flag). Two households in contact interact only if |x_i - x_j| < d; then x_i += mu (x_j - x_i) and x_j += mu (x_i - x_j).
• The update is symmetric, so the mean opinion is conserved exactly. With d of 0.5 or more everybody converges to one opinion; for smaller d several clusters survive, roughly 1 / (2 d) of them.

Checks run in the page

• Random start: the measured same-group share equals the random-mixing expectation and the household count equals round((1 - empty share) x lots).
• Schelling run to convergence with tolerance 37.5 %: the index rises well above its random value while the number of households stays constant; with tolerance 0 nobody ever moves.
• Bounded confidence: the mean opinion is conserved to 1e-9; d = 0.5 gives exactly 1 cluster and d = 0.12 gives at least 3.

Honest simplifications

• These are toy models. Real neighbourhood patterns also depend on prices, jobs, schools, history and policy, not only on personal preferences; Schelling's model shows that preferences can be sufficient for sorting, not that they are the only or main cause of it in any real place.
• The two groups are abstract roof colours, not real populations. Households have identical rules; there is no wealth, age or network structure beyond the grid.
• Opinions are one number in [0, 1]; real opinions are many-dimensional and are shaped by media, institutions and trust. The 1/(2d) cluster count is a rule of thumb from simulations, not an exact law.
• Randomness: each run uses a random seed; the sweep curves use one fixed seed, so they show typical, not average, behaviour.
• The Blender houses, trees and flags are illustrations only.

What to try

• Start with "Mild preference (33 %)", then lower tolerance step by step and watch where the town stops sorting (graph 3).
• Make blue a 20 % minority: it clusters more strongly than the majority.
• Switch to opinions, set d = 0.25 and compare "neighbours only" with "anyone in town".
• Tap a lot to plant an extreme opinion and see how far it spreads for different d.