Quantifying Emergent Behaviors in ABM and CA models using Conditional Entropy

LANET 2025 - 4th Latin American Conference on Complex Networks

This poster was presented at the 4th Latin American Conference on Complex Networks - LANET 2025 (28 July - 1 August 2025, Punta del Este, Uruguay) at Centro Universitario Regional Este, Universidad de la República. It summarizes a method to quantify visual emergent behaviors in agent-based and cellular automata systems using Mean Information Gain.

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Mean Information Gain

We introduce conditional entropy as a measure of complexity—specifically, its mean value, commonly known as the mean information gain 𝐺. To clarify how this metric can be calculated step by step from cellular automata, I created a practical guide based on an example presented in this paper:

Examples

Patterns with less structure tend to exhibit higher values of 𝐺, reflecting greater spatial disorder.

Convergent Behavior

The convergent system initially oscillates in one direction until it converges in the border.

Periodic Behavior

The periodic system quickly converges into oscillating clusters.

Complex Behavior

The complex system presents a close-to-chaotic behavior but agents tend to move together.

Chaotic Behavior

The chaotic system does not present any recognizable pattern.