Schelling segregation model

Mild preference. Severe outcome.

Two kinds of agents share a grid. Each wants only a modest fraction of its neighbours to be similar — and moves if it isn't. Run it and watch a tolerant population sort itself into hard blocks.

Tick

Happy

—%

Segregation

—%

Each agent is content if just 30% of its neighbours match. Press play — nobody wants segregation, yet it appears anyway.

Playback

Segregation index over ticks—%

segregation happy start

Parameters

Tolerance — similar neighbours wanted30%

Empty cells10%

Group split50/50

Grid size50×50

Tolerance, empty %, split and size all reset the grid. Try 20%, then 35%, then 60% — small shifts in preference, wildly different cities.

How to use

Set the tolerance slider — the share of like-neighbours each agent prefers. Press Run. The curve tracks the segregation index (fraction of same-type neighbour pairs) climbing tick by tick. Even at 30%, watch it race past 70%.

What Schelling showed

In 1971 Thomas Schelling published a model where each person prefers to live where a minimum fraction of their neighbours are "similar." Even at very mild tolerance (30%), the result is not mild — segregation collapses to near-complete separation.

This is emergence: macro behaviour (whole-neighbourhood sorting) that nobody at the micro level intended. No one in the simulation wants segregation; everyone is willing to live in a mixed neighbourhood. The system still produces it.

Try setting tolerance to 20%, then 35%, then 60%. The shift from "mild discomfort" to "moderate preference" produces wildly different macro outcomes.

What "tolerance" really means here

Each agent checks its 8 Moore neighbours. If the share of similar-type neighbours is below the tolerance threshold, the agent moves to a random empty cell. Otherwise it stays.

30% means an agent is content with 70% of its neighbours being different. Yet starting from a random arrangement, the result is roughly 70–80% same-type clustering. Mild preference → severe outcome.

Real-world parallels (with care)

Schelling's model is a thought experiment, not a complete theory of housing segregation. Real cities have explicit policies (redlining, restrictive covenants, zoning), wealth and access differences, and active discrimination — all of which dominate over weak individual preferences.

What the model does show is that even without overt discrimination, even with everyone tolerating diversity at 70%+, you can still get sharp boundaries. Individual intent is not destiny at the system level.

Citations

Schelling, T.C. (1971). "Dynamic models of segregation." Journal of Mathematical Sociology 1(2): 143–186. The original paper; Schelling received the 2005 Nobel Memorial Prize in Economic Sciences (shared with Aumann).
Schelling, T.C. (1978). Micromotives and Macrobehavior. W.W. Norton. Book-length development of the framework — neighbour-preference micromotives producing aggregate segregation.
Vinkovic, D. & Kirman, A. (2006). "A physical analogue of the Schelling model." PNAS 103(51): 19261–19265. Maps the Schelling model to a physical interface-energy analogue.
Clark, W.A.V. & Fossett, M. (2008). "Understanding the social context of the Schelling segregation model." PNAS 105(11): 4109–4114. Connects to U.S. residential-mobility empirics.

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