Aizawa Attractor
chaos · 36 views
chaos
What It Is
Aizawa 3D continuous flow with torus-like topology and two polar spikes --- structurally distinct from Lorenz butterfly, Rossler spiral, and Halvorsen cyclic. Multistable. Output: x-coordinate.
Interpretation
Standard analysis sees: smooth / autocorrelated; red spectrum (low-frequency / 1-over-f power); strongly periodic; low-complexity (predictable, not noise-like); volatility-clustering (bursty); multifractal. The atlas detects no named structure beyond this. It sits beside Halvorsen Attractor in the atlas (standard-bank rank 25) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.69
asymmetry0.65
occupancy0.71
short-range corr0.86
long-range memory0.71
spectral colour0.11
periodicity0.87
complexity0.11
time-irreversibility0.68
volatility clustering0.86
multifractality0.87
dimensionality0.26
nonstationarity0.52
What the atlas adds
Nothing beyond the standard reading — this source’s structure is already captured by standard features; the atlas adds no named residual.
Composition
dtypefloat64
range[-1.427, 1.45]
unique values16222 / 16384
mean ± std-0.000723 ± 0.564
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/Aizawa_Attractor.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Aizawa_Attractor.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Aizawa_Attractor.png)
Inflation (Substitution) > barcode
/d_curve/Aizawa_Attractor.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/Aizawa_Attractor.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/Aizawa_Attractor.png)
Ulam Spiral (Sacks) > default
/default/Aizawa_Attractor.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Halvorsen Attractor | 3.25 | |
| Rossler Attractor | 3.42 | |
| Berry Random Wave | 3.57 | cross-domain |
Which Geometries Light Up
Catch24 › Catch24:SP_Summaries_welch_rect_area_5_1 | rank 4/298 | 0.9999 |
Hodge–Laplacian › Hodge–Laplacian:poisson_recovery_error | rank 4/298 | 4.6028 |
Symplectic › Symplectic:phase_volume_explored | rank 4/298 | 0.8226 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources