5-Torus Quasiperiodic
chaos · 36 views
chaos
What It Is
1D observable from dense quasiperiodic orbit on T^5 (frequencies sqrt 2,3,5,7,11). Ground-truth intrinsic dimension d=5.
Interpretation
Standard analysis sees: strongly periodic. The atlas additionally detects multi-frequency phase coupling.
What standard analysis sees
tail heaviness0.45
asymmetry0.44
occupancy0.77
short-range corr0.74
long-range memory0.20
spectral colour0.32
periodicity0.91
complexity0.17
time-irreversibility0.62
volatility clustering0.73
multifractality0.63
dimensionality0.52
nonstationarity0.16
What the atlas adds
multi-frequency phase coupling+4.7z
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
Symplectic:phase_volume_explored | +2.0z | bank-miss 1.1σ |
Composition
dtypefloat64
range[-2.184, 2.183]
unique values16384 / 16384
mean ± std0.000257 ± 0.856
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/5-Torus_Quasiperiodic.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/5-Torus_Quasiperiodic.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/5-Torus_Quasiperiodic.png)
Inflation (Substitution) > barcode
/d_curve/5-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/5-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/5-Torus_Quasiperiodic.png)
Ulam Spiral (Sacks) > default
/default/5-Torus_Quasiperiodic.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| 4-Torus Quasiperiodic | 1.20 | |
| 3-Torus Quasiperiodic | 1.76 | |
| Ruelle-Takens Cascade | 2.73 |
Which Geometries Light Up
Bispectrum › Bispectrum:off_diagonal_ratio | rank 1/298 | 1.0000 |
Bispectrum › Bispectrum:bicoherence_concentration | rank 3/298 | 0.9748 |
Boltzmann › Boltzmann:nn_dominance | rank 5/298 | 3.7602 |
Septagonal (Danzer) › Septagonal (Danzer):z_conjugate | rank 5/298 | 0.6347 |
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