4-Torus Quasiperiodic
chaos · 36 views
chaos
What It Is
1D observable from dense quasiperiodic orbit on T^4 (frequencies sqrt 2,3,5,7). Ground-truth intrinsic dimension d=4 --- past typical GP correlation-dim horizon.
Interpretation
Standard analysis sees: strongly periodic. The atlas additionally detects multi-frequency phase coupling.
What standard analysis sees
tail heaviness0.44
asymmetry0.45
occupancy0.80
short-range corr0.75
long-range memory0.20
spectral colour0.35
periodicity0.92
complexity0.16
time-irreversibility0.61
volatility clustering0.74
multifractality0.66
dimensionality0.48
nonstationarity0.15
What the atlas adds
multi-frequency phase coupling+4.3z
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 1.2σ |
AutoRegressive:ar_coef_8 | +2.2z | bank-miss 2.7σ |
Symplectic:phase_volume_explored | +2.1z | bank-miss 1.2σ |
Composition
dtypefloat64
range[-2.075, 1.995]
unique values16384 / 16384
mean ± std0.00017 ± 0.845
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/4-Torus_Quasiperiodic.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/4-Torus_Quasiperiodic.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/4-Torus_Quasiperiodic.png)
Inflation (Substitution) > barcode
/d_curve/4-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/4-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/4-Torus_Quasiperiodic.png)
Ulam Spiral (Sacks) > default
/default/4-Torus_Quasiperiodic.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| 3-Torus Quasiperiodic | 1.19 | |
| 5-Torus Quasiperiodic | 1.20 | |
| Ruelle-Takens Cascade | 2.60 |
Which Geometries Light Up
AutoRegressive › AutoRegressive:ar_coef_1 | rank 4/298 | 2.5265 |
Bispectrum › Bispectrum:off_diagonal_ratio | rank 3/298 | 0.9639 |
Bispectrum › Bispectrum:bicoherence_concentration | rank 5/298 | 0.9684 |
Chladni › Chladni:modal_nodal_cascade | rank 294/298 | -0.4284 |
Fractal (Mandelbrot) › Fractal (Mandelbrot):escape_time_variance | rank 5/298 | 910.3091 |
Isochronicity › Isochronicity:frequency_shear | rank 4/298 | 0.8560 |
Septagonal (Danzer) › Septagonal (Danzer):z_conjugate | rank 1/298 | 0.7680 |
Septagonal (Danzer) › Septagonal (Danzer):cubic_coherence | rank 4/298 | 0.2261 |
Symplectic › Symplectic:phase_volume_explored | rank 5/298 | 0.8116 |
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