Ikeda Map
iterated-maps · 37 views
iterated-mapschaotic
What It Is
Laser cavity chaos: x(n+1) = 1 + u(x cos t - y sin t), y(n+1) = u(x sin t + y cos t) where t = 0.4 - 6/(1+x²+y²). Multistable at u=0.9, different attractor topology from Hénon
Interpretation
Standard analysis sees: rich, high-entropy values; anti-persistent; blue spectrum (high-frequency power); aperiodic / broadband; time-irreversible (sharp rises, slow decay); high-dimensional / space-filling. The atlas additionally detects discrete-map sensitive dependence. It sits beside Gzip (level 9) in the atlas (standard-bank rank 42) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.37
asymmetry0.39
occupancy0.87
short-range corr0.18
long-range memory0.13
spectral colour0.90
periodicity0.13
complexity0.59
time-irreversibility0.93
volatility clustering0.40
multifractality0.15
dimensionality0.99
nonstationarity0.36
What the atlas adds
discrete-map sensitive dependence+3.1z
deterministic chaos (positive λ_max, sensitive dependence)
names a discrete-map-scoped estimate, NOT chaos in general — continuous-flow chaos (Lorenz, Rössler) reads weak/neutral here despite being genuinely chaotic; spiky arithmetic sources can false-positive on the finite-time estimateAtlas-extreme metrics the standard bank can’t predict for this source
Nonstationarity:change_quantiles_low | +3.2z | bank-miss 1.2σ |
Predictability:entropy_decay_rate | +2.2z | bank-miss 1.8σ |
Composition
dtypefloat64
range[-0.3022, 1.606]
unique values16222 / 16384
mean ± std0.628 ± 0.482
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/Ikeda_Map.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Ikeda_Map.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Ikeda_Map.png)
Inflation (Substitution) > barcode
/d_curve/Ikeda_Map.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/Ikeda_Map.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/Ikeda_Map.png)
Ulam Spiral (Sacks) > default
/default/Ikeda_Map.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Clifford Attractor | 3.68 | |
| Wigner Semicircle | 3.92 | cross-origin |
| Gzip (level 9) | 3.92 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:CO_trev_1_num | rank 5/307 | 2.1401 |
Klein Bottle › Klein Bottle:rank_deficit_max | rank 303/307 | 0.1026 |
Klein Bottle › Klein Bottle:rank_deficit | rank 306/307 | 0.0475 |
Möbius-S³ › Möbius-S³:sector_transition_entropy | rank 4/307 | 0.6100 |
Nonstationarity › Nonstationarity:change_quantiles_low | rank 4/307 | 0.1150 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):bingham_concentration | rank 305/307 | 0.4500 |
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