Evidence for the Edge of Chaos: A Multi-Scale Compression Analysis

This manuscript presents a comprehensive investigation into systems exhibiting critical transitions characteristic of “edge of chaos” behaviour, employing an innovative multi-scale compression analysis. The study demonstrates the effectiveness of compression-based methodologies (disk compression and in-memory algorithms: GZIP, BZ2, LZMA) as sensitive detectors for identifying transitions between ordered and chaotic states.

Key findings include:

• Extraordinary compression ratios (up to 860×) signifying global order.

• Non-monotonic trends in chaos metrics (Lyapunov exponents, spectral flatness, autocorrelation decay) revealing critical phase transitions.

• Emergent complexity evidenced by accelerating increases in sample entropy across scales.

These results offer robust empirical validation of edge-of-chaos behaviour and contribute to broader discussions on self-organised criticality, meta-criticality, and the informational properties of complex adaptive systems. This research is particularly relevant for those interested in nonlinear dynamics, complexity theory, chaos theory, information theory, and computational methods for analysing complex systems.