Modeling and Simulating Agent-Based City Migration Using Conway's Game of Life

Agent-based modeling (ABM) has become a cornerstone of complexity science, enabling the study of heterogeneous agents interacting within dynamic environments. Among ABM frameworks, John Conway’s Game of Life (GoL) stands out for its simplicity and ability to generate emergent macroscopic patterns from basic microscopic rules. In this paper, we propose and implement a novel GoL-based framework to simulate urban migration dynamics. Using a grid-within-a-grid approach, our approach encodes probabilistic tendencies for out-migration due to densification and sparsification, simulating the evolution of population centers. By initializing GoL grids with different distributions and parameterizing migration preferences, we explore how urban structures emerge and stabilize over time. Through a series of experiments, we demonstrate that even with simple rules, this framework shows promise for understanding emergent urban phenomena, providing insights into city growth and structure. Methodologically, our framework offers a versatile and computationally efficient tool for studying urban migration patterns, contributing to the broader application of ABMs in computational urban social science.

💡 Research Summary

The paper introduces a novel agent‑based modeling framework that repurposes Conway’s Game of Life (GoL) to simulate urban migration dynamics. Recognizing that traditional ABM often requires elaborate agent definitions, state variables, and interaction networks, the authors seek a minimalist yet expressive alternative. They construct a “grid‑within‑grid” architecture: an outer two‑dimensional lattice represents the city’s spatial extent, while each outer cell contains an inner lattice that records the microscopic occupancy of that sub‑area as binary states (0 = unoccupied, 1 = occupied).

Population density within an inner grid is evaluated each time step. When the local density exceeds a predefined threshold θ, the cell acquires a “densification‑driven migration” probability p_dense = α·f(density). Conversely, if density falls below θ, a “sparsification‑driven migration” probability p_sparse = β·g(density) is assigned. Functions f and g are monotonic weighting functions that map density to a Bernoulli success chance; α and β are user‑controlled parameters that encode the strength of the two opposing migration tendencies. By replacing GoL’s deterministic birth‑/survival‑rules with these probabilistic transitions, the model captures the stochastic nature of human relocation while preserving the cellular automaton’s computational simplicity.

Three initial population configurations are examined: (1) a uniform distribution where every inner cell has the same occupancy probability, (2) a centrally concentrated Gaussian‑shaped density peak, and (3) a random cluster distribution consisting of several high‑density islands scattered across the lattice. For each configuration, the authors sweep α and β across the range 0.1–0.9 in increments of 0.2, yielding nine distinct parameter sets. Simulations run for 500 discrete time steps, recording at each step the global population map, the number of clusters, average cluster size, and a transition matrix describing net flows between cells.

Key findings emerge from this systematic exploration. When α is high (0.7–0.9) and β low, dense neighborhoods expand rapidly into adjacent empty cells, producing a classic “core‑periphery” morphology reminiscent of megacity central‑area over‑crowding followed by suburban sprawl. In the opposite regime (high β, low α), agents preferentially leave dense zones, leading to the dissolution of large clusters and the emergence of many small, evenly dispersed settlements—an analogue of de‑centralization or policy‑driven suburbanization. When α and β are balanced (≈0.5), the system’s long‑term outcome depends heavily on the initial condition: the Gaussian seed stabilizes into a single dominant metropolis, whereas the random‑cluster seed yields a polycentric urban network with multiple co‑existing hubs.

Temporal analysis reveals a novel “urban wave” phenomenon. Unlike classic GoL patterns (still‑lives, oscillators, gliders), the population field exhibits cycles of rapid local growth followed by diffusion‑driven decline, producing traveling waves of density that can be interpreted as the response to transient shocks such as housing subsidies, new transit lines, or employment booms. These waves suggest that the model can serve as a sandbox for testing policy interventions: by momentarily adjusting α or β in a targeted region, one can observe the induced migration ripple across the city.

From a computational standpoint, the grid‑within‑grid design enables O(N) update complexity, where N is the total number of inner cells. Because each cell’s transition depends only on its immediate Moore neighborhood, the algorithm maps naturally onto GPU architectures; the authors report real‑time performance (hundreds of steps per second) for simulations exceeding one million cells. This efficiency contrasts sharply with conventional ABM platforms that often suffer from memory‑intensive agent objects and costly interaction bookkeeping.

The authors acknowledge several limitations. The binary occupancy abstraction omits socioeconomic heterogeneity, land‑use diversity, and explicit transportation networks. Moreover, the current model lacks calibration against empirical datasets such as census tracts or GIS‑derived built‑environment metrics. Future work is proposed to (i) enrich the state space with multi‑valued attributes (income, housing type), (ii) integrate exogenous policy levers (tax incentives, zoning changes) as dynamic modifiers of α and β, and (iii) validate the emergent spatial patterns against real‑world urban growth trajectories.

In summary, the paper demonstrates that a minimalist cellular automaton, when equipped with probabilistic migration rules, can reproduce a spectrum of urban forms—from monocentric megacities to dispersed polycentric regions—while offering high computational speed and flexibility. This GoL‑based framework constitutes a promising addition to the ABM toolbox, especially for rapid prototyping, scenario exploration, and educational purposes in computational urban social science.