Aizawa Attractor
continuous-flows · 37 views
continuous-flowschaotic
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; strongly periodic; low-complexity (predictable, not noise-like); volatility-clustering (bursty); multifractal. The atlas finds no named structure, but the source is distinctively extreme on Symplectic:phase_volume_explored (+2.2z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.66
asymmetry0.64
occupancy0.73
short-range corr0.85
long-range memory0.72
spectral colour0.16
periodicity0.86
complexity0.10
time-irreversibility0.47
volatility clustering0.85
multifractality0.88
dimensionality0.27
nonstationarity0.55
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Symplectic:phase_volume_explored | +2.2z | bank-miss 1.1σ |
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 > free_plate_nodal
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 | 3.20 | |
| Rossler Attractor | 3.36 | |
| Hénon-Heiles | 3.49 |
Which Geometries Light Up
Catch24 › Catch24:SP_Summaries_welch_rect_area_5_1 | rank 4/306 | 0.9999 |
Hodge–Laplacian › Hodge–Laplacian:poisson_recovery_error | rank 4/306 | 4.6028 |
Symplectic › Symplectic:phase_volume_explored | rank 4/306 | 0.8226 |
in algorithmic-bytesChua's Circuit →
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources