Noisy Period-2
iterated-maps · 37 views
iterated-mapsperiodic
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. The atlas finds no named structure, but the source is distinctively extreme on Heisenberg (Nil) (centered):area_length_ratio (+5.8z) — beyond what the standard bank predicts for it. It sits beside Aliquot Orbit Lengths in the atlas (standard-bank rank 40) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.14
asymmetry0.39
occupancy0.67
short-range corr0.02
long-range memory0.16
spectral colour0.75
periodicity0.97
complexity0.36
time-irreversibility0.49
volatility clustering0.20
multifractality0.23
dimensionality0.42
nonstationarity0.20
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Heisenberg (Nil) (centered):area_length_ratio | +5.8z | bank-miss 1.3σ |
Heisenberg (Nil) (centered):xy_spread | +5.2z | bank-miss 1.9σ |
Predictability:entropy_decay_rate | +2.8z | bank-miss 2.8σ |
S² × ℝ (Thurston):great_circle_dispersion | +2.7z | bank-miss 2.1σ |
Boltzmann:spectral_gap_J | -2.6z | bank-miss 1.9σ |
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 > free_plate_nodal
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 | 4.64 | cross-origin |
| Aliquot Orbit Lengths | 4.84 | cross-origin |
| Blue Noise | 4.90 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:CO_f1ecac | rank 302/306 | 0.3405 |
Fisher Information › Fisher Information:effective_dimension | rank 302/306 | 2.6263 |
Fractal (Mandelbrot) › Fractal (Mandelbrot):escape_entropy | rank 1/306 | 3.4422 |
H4 600-Cell › H4 600-Cell:lattice_closure | rank 2/306 | 1.0000 |
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):area_length_ratio | rank 5/306 | 0.3566 |
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):xy_spread | rank 5/306 | 4378.3324 |
Hölder Regularity › Hölder Regularity:holder_mean | rank 302/306 | -1.6842 |
Laplacian › Laplacian:biharmonic_ratio | rank 4/306 | 15.7413 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 4/306 | 0.1033 |
Predictability › Predictability:entropy_decay_rate | rank 4/306 | 0.1351 |
SL(2,ℝ) (Thurston) › SL(2,ℝ) (Thurston):mean_trace | rank 303/306 | -1.7273 |
Symplectic › Symplectic:phase_reflection_symmetry | rank 305/306 | -0.0992 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):great_circle_dispersion | rank 5/306 | 2.4197 |
Ulam Spiral (Square) › Ulam Spiral (Square):radon_anisotropy | rank 302/306 | 0.0003 |
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