2-Torus Quasiperiodic
chaos · 36 views
chaos
What It Is
1D observable from dense quasiperiodic orbit on T^2 (frequencies sqrt 2, sqrt 3). Ground-truth intrinsic dimension d=2. Ergodic but not mixing.
Interpretation
Standard analysis sees: rich, high-entropy values; strongly periodic; low-complexity (predictable, not noise-like); stationary. The atlas finds no named structure, but the source is distinctively extreme on Spirograph:petal_symmetry (+3.5z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.34
asymmetry0.46
occupancy0.89
short-range corr0.76
long-range memory0.23
spectral colour0.36
periodicity0.94
complexity0.14
time-irreversibility0.58
volatility clustering0.74
multifractality0.60
dimensionality0.35
nonstationarity0.12
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Spirograph:petal_symmetry | +3.5z | bank-miss 1.2σ |
Bispectrum:bicoherence_concentration | -2.3z | bank-miss 2.3σ |
Composition
dtypefloat64
range[-1.499, 1.5]
unique values16384 / 16384
mean ± std4.12e-06 ± 0.792
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/2-Torus_Quasiperiodic.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/2-Torus_Quasiperiodic.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/2-Torus_Quasiperiodic.png)
Inflation (Substitution) > barcode
/d_curve/2-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/2-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/2-Torus_Quasiperiodic.png)
Ulam Spiral (Sacks) > default
/default/2-Torus_Quasiperiodic.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| 3-Torus Quasiperiodic | 2.62 | |
| 4-Torus Quasiperiodic | 2.98 | |
| 5-Torus Quasiperiodic | 3.40 |
Which Geometries Light Up
Chladni › Chladni:modal_nodal_cascade | rank 296/298 | -0.4942 |
Higher-Order Statistics › Higher-Order Statistics:c3_energy | rank 294/298 | 0.0004 |
Isochronicity › Isochronicity:frequency_shear | rank 1/298 | 0.9604 |
Moiré › Moiré:moire_invariance_breadth | rank 298/298 | 0.0025 |
Navier-Stokes › Navier-Stokes:sl_fit_quality | rank 297/298 | -0.9987 |
Septagonal (Danzer) › Septagonal (Danzer):cubic_coherence | rank 2/298 | 0.2771 |
Septagonal (Danzer) › Septagonal (Danzer):z_conjugate | rank 3/298 | 0.7125 |
Sol (Thurston) › Sol (Thurston):path_length | rank 295/298 | 21730.2379 |
Spirograph › Spirograph:petal_symmetry | rank 3/298 | 0.6806 |
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