Quantum Walk
quantum · 36 views
quantum
What It Is
Hadamard walk on a 257-site ring --- coin polarization ⟨σ_z(t)⟩ with ongoing wraparound dynamics and quantum recurrences
Interpretation
Standard analysis sees: anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power). The atlas finds no named structure, but the source is distinctively extreme on AutoRegressive:ar_coef_3 (-4.2z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.68
asymmetry0.54
occupancy0.37
short-range corr0.10
long-range memory0.05
spectral colour0.93
periodicity0.38
complexity0.78
time-irreversibility0.40
volatility clustering0.40
multifractality0.35
dimensionality0.82
nonstationarity0.37
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
AutoRegressive:ar_coef_3 | -4.2z | bank-miss 1.4σ |
Gottwald-Melbourne:k_variance | +3.9z | bank-miss 1.4σ |
Chladni:modal_nodal_cascade | +3.7z | bank-miss 1.3σ |
Nonstationarity:adf_pvalue | +3.4z | bank-miss 3.8σ |
AutoRegressive:ar_coef_1 | -2.7z | bank-miss 2.2σ |
Navier-Stokes:ess_quality | +2.0z | bank-miss 2.1σ |
Composition
dtypefloat64
range[-0.1362, 0]
unique values16384 / 16384
mean ± std-0.0798 ± 0.00718
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/Quantum_Walk.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Quantum_Walk.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Quantum_Walk.png)
Inflation (Substitution) > barcode
/d_curve/Quantum_Walk.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/Quantum_Walk.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/Quantum_Walk.png)
Ulam Spiral (Sacks) > default
/default/Quantum_Walk.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| IMS Bearing Degraded | 4.70 | cross-domain |
| Hofstadter Q | 4.75 | cross-domain |
| Coupled Map Lattice | 4.83 | cross-domain |
Which Geometries Light Up
AutoRegressive › AutoRegressive:ar_coef_1 | rank 297/298 | -1.6779 |
Chladni › Chladni:modal_nodal_cascade | rank 1/298 | 2.1487 |
Laplacian › Laplacian:poisson_recovery_error | rank 1/298 | 16.0328 |
Möbius-S³ › Möbius-S³:phase_profile_deviation | rank 298/298 | 0.1072 |
Navier-Stokes › Navier-Stokes:ess_quality | rank 4/298 | 0.9891 |
Spirograph › Spirograph:petal_symmetry | rank 2/298 | 0.6825 |
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