Symbolic Lorenz
continuous-flows · 37 views
continuous-flowschaotic
What It Is
Lorenz attractor reduced to a binary symbol stream (left lobe vs right lobe), one symbol per half-orbit. The symbolic itinerary encodes the topological structure of chaos
Interpretation
Standard analysis sees: bounded / light-tailed; few distinct values; multifractal; stationary. The atlas finds no named structure, but the source is distinctively extreme on Spherical S²:angular_spread (+3.1z) — beyond what the standard bank predicts for it. It sits beside Rule 30 in the atlas (standard-bank rank 61) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.01
asymmetry0.47
occupancy0.07
short-range corr0.49
long-range memory0.48
spectral colour0.49
periodicity0.23
complexity0.28
time-irreversibility0.51
volatility clustering0.51
multifractality0.86
dimensionality0.67
nonstationarity0.10
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Spherical S²:angular_spread | +3.1z | bank-miss 1.3σ |
Möbius-S³:sector_transition_entropy | -2.6z | bank-miss 1.2σ |
Composition
dtypefloat64
range[0, 1]
unique values2 / 16384
mean ± std0.509 ± 0.5
Binary sequence — two distinct symbols.
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/Symbolic_Lorenz.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Symbolic_Lorenz.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Symbolic_Lorenz.png)
Inflation (Substitution) > barcode
/d_curve/Symbolic_Lorenz.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/Symbolic_Lorenz.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/Symbolic_Lorenz.png)
Ulam Spiral (Sacks) > default
/default/Symbolic_Lorenz.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Liouville Function | 3.02 | cross-origin |
| Rule 30 | 3.46 | cross-origin |
| Morse Code | 3.74 | cross-origin |
Which Geometries Light Up
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):temporal_variance | rank 5/306 | 17.7651 |
Mostow Rigidity › Mostow Rigidity:distance_rigidity | rank 3/306 | 0.9843 |
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_fine | rank 2/306 | 0.2599 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources