Halvorsen Attractor
continuous-flows · 37 views
continuous-flowschaotic
What It Is
Halvorsen x-coordinate --- 3-fold cyclically symmetric chaotic flow: each axis obeys the same equation with cyclic substitution. Topologically a 'cyclic transport' attractor, distinct from Lorenz switching or Rossler spiral.
Interpretation
Standard analysis sees: smooth / autocorrelated; red spectrum (low-frequency / 1-over-f power); low-complexity (predictable, not noise-like); time-irreversible (slow rise, sharp collapse); volatility-clustering (bursty). The atlas detects no named structure beyond this.
What standard analysis sees
tail heaviness0.42
asymmetry0.64
occupancy0.84
short-range corr0.88
long-range memory0.79
spectral colour0.03
periodicity0.70
complexity0.10
time-irreversibility0.07
volatility clustering0.87
multifractality0.78
dimensionality0.30
nonstationarity0.54
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[-12.78, 5.844]
unique values16222 / 16384
mean ± std-3.24 ± 4.38
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/Halvorsen_Attractor.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Halvorsen_Attractor.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Halvorsen_Attractor.png)
Inflation (Substitution) > barcode
/d_curve/Halvorsen_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/Halvorsen_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/Halvorsen_Attractor.png)
Ulam Spiral (Sacks) > default
/default/Halvorsen_Attractor.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Lorenz-96 N=8 | 2.75 | |
| Lorenz-96 N=4 F=16 | 2.81 | |
| Lorenz-96 N=36 | 2.91 |
Which Geometries Light Up
Fractal (Mandelbrot) › Fractal (Mandelbrot):escape_time_variance | rank 2/307 | 914.4082 |
Hodge–Laplacian › Hodge–Laplacian:poisson_recovery_error | rank 3/307 | 4.7706 |
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