complexity-science

What problem does it solve?

This skill helps you rigorously analyze complex systems by fitting heavy-tailed distributions, quantifying long-range dependence, measuring fractal structure, and simulating emergent dynamics.

Core Features & Use Cases

• Power-law fitting & testing: Estimate scaling exponents and statistically compare power-law fit versus alternatives (e.g., lognormal, exponential).
• Time-series and structure complexity: Compute the Hurst exponent, sample entropy, and fractal dimension via box-counting.
• Network and dynamical modeling: Estimate bond percolation thresholds and run agent-based models (Schelling segregation) using Mesa.
• Information-theoretic analysis: Compute Shannon entropy, mutual information, joint entropy, and normalized mutual information to relate signals.
• Use case: Given a citation network degree sequence and a time series of an evolving metric, use this skill to test whether connectivity is scale-free, quantify temporal persistence, and compare dependencies between two processes.

Quick Start

Ask your AI agent to analyze a degree sequence for power-law behavior, estimate Hurst exponent and sample entropy for a time series, and run a Schelling segregation simulation to quantify emergent ordering.