3-Torus Quasiperiodic
chaos · 36 views
chaos
What It Is
1D observable from dense quasiperiodic orbit on T^3 (frequencies sqrt 2, sqrt 3, sqrt 5). Ground-truth intrinsic dimension d=3.
Interpretation
Standard analysis sees: rich, high-entropy values; strongly periodic. The atlas additionally detects multi-frequency phase coupling.
What standard analysis sees
tail heaviness0.41
asymmetry0.48
occupancy0.85
short-range corr0.76
long-range memory0.21
spectral colour0.36
periodicity0.93
complexity0.15
time-irreversibility0.57
volatility clustering0.74
multifractality0.65
dimensionality0.44
nonstationarity0.16
What the atlas adds
multi-frequency phase coupling+2.9z
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
Isochronicity:frequency_shear | +2.6z | bank-miss 1.3σ |
Composition
dtypefloat64
range[-1.83, 1.817]
unique values16384 / 16384
mean ± std0.000102 ± 0.826
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/3-Torus_Quasiperiodic.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/3-Torus_Quasiperiodic.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/3-Torus_Quasiperiodic.png)
Inflation (Substitution) > barcode
/d_curve/3-Torus_Quasiperiodic.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/3-Torus_Quasiperiodic.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/3-Torus_Quasiperiodic.png)
Ulam Spiral (Sacks) > default
/default/3-Torus_Quasiperiodic.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| 4-Torus Quasiperiodic | 1.19 | |
| 5-Torus Quasiperiodic | 1.76 | |
| 2-Torus Quasiperiodic | 2.62 |
Which Geometries Light Up
Bispectrum › Bispectrum:coupling_frequency_centroid | rank 294/298 | 0.2962 |
Isochronicity › Isochronicity:frequency_shear | rank 3/298 | 0.8607 |
Ordinal Partition › Ordinal Partition:time_irreversibility | rank 294/298 | 0.0069 |
Septagonal (Danzer) › Septagonal (Danzer):z_conjugate | rank 4/298 | 0.6871 |
Symplectic › Symplectic:phase_volume_explored | rank 3/298 | 0.8276 |
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