📊 Data Analysis¶

Utilities and scripts for processing, visualizing, and statistically evaluating results from the simulation models.

📐 Information-Theoretic Measures (`info_measures.py`)¶

A reusable library for quantifying emergence in any simulation. These measures operationalise the dimensions of the System Intelligence Index.

Spatial measures¶

Function	What it measures
`shannon_entropy(field)`	Disorder / unpredictability of the field
`spatial_mutual_information(field)`	How much a cell reveals about its neighbours
`block_entropy(field, k)`	Multi-scale spatial correlations

Temporal measures¶

Function	What it measures
`time_series_entropy(x)`	Temporal unpredictability
`transfer_entropy(source, target)`	Causal information flow X → Y
`active_information_storage(x)`	How much a process "remembers"

Emergence measures¶

Function	What it measures
`integration(field)`	Whole > sum of parts (simplified Φ)
`complexity_measure(field)`	Multi-scale structure (TSE complexity)

Quick analysis¶

from info_measures import analyse_field
results = analyse_field(my_field, name="My Simulation")

🔬 Comparative Analysis (`analyse_emergence.py`)¶

Runs a full analysis across multiple systems (noise, Game of Life, Reaction-Diffusion, Sandpile) and outputs:

Per-system entropy, MI, integration, and complexity
Comparative bar chart saved to emergence_analysis.png

cd data-analysis
python3 analyse_emergence.py

Why This Matters¶

Most claims about "emergence" in complex systems remain qualitative. These tools make it possible to measure emergence and compare systems on a common scale – the first step toward a rigorous, quantitative theory of system intelligence.