4-Torus Quasiperiodic
coupled-oscillators · 37 views
coupled-oscillatorsquasiperiodic
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: red spectrum (low-frequency / 1-over-f power); strongly periodic; stationary. The atlas finds no named structure, but the source is distinctively extreme on Bispectrum:off_diagonal_ratio (+4.1z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.44
asymmetry0.45
occupancy0.82
short-range corr0.75
long-range memory0.23
spectral colour0.13
periodicity0.91
complexity0.18
time-irreversibility0.49
volatility clustering0.74
multifractality0.67
dimensionality0.51
nonstationarity0.14
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Bispectrum:off_diagonal_ratio | +4.1z | bank-miss 1.8σ |
Isochronicity:frequency_shear | +2.4z | bank-miss 1.5σ |
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 > free_plate_nodal
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 | |
|---|---|---|
| 5-Torus Quasiperiodic | 1.25 | |
| 3-Torus Quasiperiodic | 1.50 | |
| Ruelle-Takens Cascade | 2.50 | cross-origin |
Which Geometries Light Up
Bispectrum › Bispectrum:off_diagonal_ratio | rank 3/306 | 0.9348 |
Chladni › Chladni:modal_nodal_cascade | rank 302/306 | -0.4262 |
Fractal (Mandelbrot) › Fractal (Mandelbrot):escape_time_variance | rank 5/306 | 910.0793 |
Isochronicity › Isochronicity:frequency_shear | rank 4/306 | 0.8560 |
Ordinal Partition › Ordinal Partition:time_irreversibility | rank 302/306 | 0.0099 |
Septagonal (Danzer) › Septagonal (Danzer):z_conjugate | rank 1/306 | 0.7828 |
Septagonal (Danzer) › Septagonal (Danzer):cubic_coherence | rank 4/306 | 0.2262 |
Symplectic › Symplectic:phase_volume_explored | rank 5/306 | 0.8112 |
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