What Is the Schelling Segregation Model?
Thomas Schelling's 1971 segregation model demonstrates that a population can self-segregate spatially even when no individual prefers segregation. Each agent has mild same-type preferences — they want only a minority of their immediate neighbors to share their type — and yet the aggregate outcome is sharply segregated neighborhoods.
The model is widely cited as the founding example of computational social science and emergence in the social sciences. It is also a cautionary example: you cannot infer individual prejudice from aggregate segregation. Mild preferences suffice.
How It Works
- Place agents of two types randomly on a grid with some empty cells.
- Each agent inspects its Moore neighborhood (8 surrounding cells) and counts the fraction of neighbors that share its type.
- If the fraction is below the similarity threshold, the agent is unhappy and moves to a random empty cell.
- Repeat until no agent wants to move, or a step budget is reached.
The Tipping Point
The most striking result in Schelling's model is the sharp phase transition around a similarity threshold of about 0.30 on a standard grid. Below this, the grid stays mixed. Above it, complete sorting into same-type neighborhoods emerges within tens of steps. The transition is surprisingly abrupt and robust across parameter variations.
What the Segregation Index Measures
The segregation index is the average, across all agents, of the fraction of neighbors that share the agent's type. In a fully mixed grid it starts at ~0.5. After convergence at a high threshold it reaches ~0.95. The index captures spatial sorting even when the population is equal-sized across both groups.
Why It Matters Fifty Years Later
Schelling's model changed how social scientists think about aggregate outcomes. Before Schelling, segregation was viewed primarily as evidence of strong preference or explicit policy. After Schelling, it became clear that weak preferences plus local dynamics suffice. The same logic has since been applied to wealth concentration, opinion polarization, and cultural clustering.
The interactive simulator below lets you move the similarity threshold and density sliders yourself. Watch the tipping point live — it is more striking in motion than in any summary statistic.