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Chaos Theory Analysis

Chaos analysis helps distinguish genuinely random behavior from deterministic systems that only look random.

Implemented in openentropy_core::chaos.

Hurst Exponent

Section titled “Hurst Exponent”

Measures long-range dependence (R/S analysis).

  • H ~= 0.5: random-walk-like
  • H > 0.5: persistent trend behavior
  • H < 0.5: anti-persistent behavior

Lyapunov Exponent

Section titled “Lyapunov Exponent”

Measures sensitivity to initial conditions.

  • lambda ~= 0: no clear deterministic chaos signature
  • lambda > 0: chaotic divergence
  • lambda < 0: convergent behavior

Correlation Dimension

Section titled “Correlation Dimension”

Measures attractor dimensionality.

  • High D2 suggests high-dimensional/random-like behavior
  • Low D2 can indicate deterministic low-dimensional structure

BiEntropy

Section titled “BiEntropy”

Measures entropy persistence through derivative levels of the bitstream.

  • Higher values indicate stronger disorder and less structure

Epiplexity

Section titled “Epiplexity”

Compression-ratio complexity metric.

  • Ratio near 1.0 indicates incompressible/random-like data
  • Lower ratios imply compressible structure
Section titled “Related”