Rössler Hyperchaos
chaos · 36 views
chaos
What It Is
4D Rössler hyperchaotic system with two positive Lyapunov exponents --- qualitatively different from standard chaos, simultaneous expansion in two directions
Interpretation
Standard analysis sees: no strongly notable standard properties. The atlas additionally detects multi-frequency phase coupling. It sits beside EEG Seizure in the atlas (standard-bank rank 89) — a neighbor conventional features miss.
What the atlas adds
multi-frequency phase coupling+3.6z
quadratic phase coupling between distinct frequencies — multiple incommensurate tones interacting (quasiperiodic / multi-tone)
Atlas-extreme metrics the standard bank can’t predict for this source
Zipf–Mandelbrot (8-bit):entropy_nonstationarity | +4.1z | bank-miss 1.8σ |
Nonstationarity:vol_of_vol | +3.4z | bank-miss 2.0σ |
Visibility Graph:assortativity | +3.3z | bank-miss 2.4σ |
Chladni:temporal_burstiness | +3.1z | bank-miss 2.1σ |
Fisher Information:velocity_spectral_gini | +2.8z | bank-miss 2.1σ |
Nonstationarity:metric_volatility | -2.0z | bank-miss 1.4σ |
Composition
dtypefloat64
range[-3.387, 6.086]
unique values16222 / 16384
mean ± std0.982 ± 1.81
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Rössler_Hyperchaos.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Rössler_Hyperchaos.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Rössler_Hyperchaos.png)
Inflation (Substitution) > barcode
/d_curve/Rössler_Hyperchaos.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Rössler_Hyperchaos.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Rössler_Hyperchaos.png)
Ulam Spiral (Sacks) > default
/default/Rössler_Hyperchaos.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| EEG Seizure | 4.83 | cross-domain |
| EEG Healthy | 4.95 | cross-domain |
| EEG Eyes Closed | 5.03 | cross-domain |
Which Geometries Light Up
Bispectrum › Bispectrum:off_diagonal_ratio | rank 4/298 | 0.8900 |
Catch24 › Catch24:SC_FluctAnal_2_rsrangefit_50_1_logi_prop_r1 | rank 1/298 | 0.8800 |
Catch24 › Catch24:SC_FluctAnal_2_dfa_50_1_2_logi_prop_r1 | rank 3/298 | 0.8080 |
Fisher Information › Fisher Information:velocity_spectral_gini | rank 1/298 | 0.8345 |
Gottwald-Melbourne › Gottwald-Melbourne:k_statistic | rank 1/298 | 0.9995 |
Moiré › Moiré:moire_peak_alpha | rank 296/298 | 0.7469 |
Möbius-S³ › Möbius-S³:hopf_fiber_coherence | rank 1/298 | 0.8264 |
Nonstationarity › Nonstationarity:vol_of_vol | rank 5/298 | 2.4061 |
Visibility Graph › Visibility Graph:assortativity | rank 2/298 | 0.7608 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):entropy_nonstationarity | rank 4/298 | 0.5616 |
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