Noisy Period-2
chaos · 36 views
chaos
What It Is
Period-2 oscillation corrupted by additive noise --- deterministic alternation partially washed out by Gaussian perturbation, bridging periodic and stochastic regimes
Interpretation
Standard analysis sees: bounded / light-tailed; anti-correlated (alternating); strongly periodic; monofractal. The atlas finds no named structure, but the source is distinctively extreme on Heisenberg (Nil) (centered):area_length_ratio (+6.1z) — beyond what the standard bank predicts for it. It sits beside Aliquot Orbit Lengths in the atlas (standard-bank rank 46) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.12
asymmetry0.37
occupancy0.61
short-range corr0.01
long-range memory0.16
spectral colour0.77
periodicity0.97
complexity0.35
time-irreversibility0.58
volatility clustering0.25
multifractality0.06
dimensionality0.33
nonstationarity0.17
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Heisenberg (Nil) (centered):area_length_ratio | +6.1z | bank-miss 1.4σ |
Heisenberg (Nil) (centered):xy_spread | +5.4z | bank-miss 2.1σ |
S² × ℝ (Thurston):great_circle_dispersion | +2.8z | bank-miss 1.4σ |
Predictability:entropy_decay_rate | +2.8z | bank-miss 2.3σ |
Boltzmann:spectral_gap_J | -2.7z | bank-miss 1.8σ |
Chladni:plate_low_mode_fraction | -2.5z | bank-miss 1.2σ |
Composition
dtypefloat64
range[-0.957, 239.3]
unique values16384 / 16384
mean ± std123 ± 63
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/Noisy_Period-2.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Noisy_Period-2.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Noisy_Period-2.png)
Inflation (Substitution) > barcode
/d_curve/Noisy_Period-2.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/Noisy_Period-2.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/Noisy_Period-2.png)
Ulam Spiral (Sacks) > default
/default/Noisy_Period-2.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Euler Totient Ratio | 4.82 | cross-domain |
| Aliquot Orbit Lengths | 5.18 | cross-domain |
| Blue Noise | 5.30 | cross-domain |
Which Geometries Light Up
Catch24 › Catch24:CO_f1ecac | rank 294/298 | 0.3376 |
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):area_length_ratio | rank 5/298 | 0.3625 |
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):xy_spread | rank 5/298 | 4421.9076 |
Hölder Regularity › Hölder Regularity:holder_mean | rank 294/298 | -1.7325 |
Laplacian › Laplacian:biharmonic_ratio | rank 4/298 | 15.7704 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 5/298 | 0.1028 |
Persistent Homology › Persistent Homology:max_lifetime | rank 296/298 | 0.5630 |
Predictability › Predictability:entropy_decay_rate | rank 4/298 | 0.1363 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):mean_trace | rank 297/298 | -1.9931 |
Symplectic › Symplectic:phase_reflection_symmetry | rank 298/298 | -0.0866 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):great_circle_dispersion | rank 5/298 | 2.4878 |
Ulam Spiral (Square) › Ulam Spiral (Square):radon_anisotropy | rank 295/298 | 0.0003 |
p-Variation › p-Variation:increment_persistence | rank 295/298 | -0.9658 |
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