Symbolic Henon
iterated-maps · 37 views
iterated-mapschaotic
What It Is
Henon map reduced to a binary symbol stream (x < 0 or x > 0) --- the symbolic itinerary of a 2D strange attractor, encoding its topological horseshoe structure
Interpretation
Standard analysis sees: bounded / light-tailed; left-skewed; few distinct values; blue spectrum (high-frequency power); homoskedastic; monofractal; stationary. The atlas finds no named structure, but the source is distinctively extreme on Hyperbolic (Poincaré):temporal_variance (+4.5z) — beyond what the standard bank predicts for it. It sits beside Collatz Parity in the atlas (standard-bank rank 22) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.09
asymmetry0.05
occupancy0.02
short-range corr0.17
long-range memory0.16
spectral colour0.89
periodicity0.23
complexity0.30
time-irreversibility0.48
volatility clustering0.09
multifractality0.13
dimensionality0.53
nonstationarity0.14
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Hyperbolic (Poincaré):temporal_variance | +4.5z | bank-miss 1.5σ |
H² × ℝ (Thurston):hyperbolic_step_dispersion | +2.8z | bank-miss 1.1σ |
Modular Residue:occupancy_entropy | -2.4z | bank-miss 1.5σ |
Composition
dtypefloat64
range[0, 1]
unique values2 / 16384
mean ± std0.667 ± 0.471
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_Henon.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Symbolic_Henon.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Symbolic_Henon.png)
Inflation (Substitution) > barcode
/d_curve/Symbolic_Henon.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_Henon.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_Henon.png)
Ulam Spiral (Sacks) > default
/default/Symbolic_Henon.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Collatz Parity | 3.40 | cross-origin |
| Rule 30 | 3.49 | cross-origin |
| Liouville Function | 3.60 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:SC_FluctAnal_2_rsrangefit_50_1_logi_prop_r1 | rank 306/307 | 0.1200 |
G2 Root System › G2 Root System:pair_angle_kurtosis | rank 304/307 | -1.9967 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):temporal_variance | rank 4/307 | 18.2333 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_step_dispersion | rank 3/307 | 7.7290 |
Mostow Rigidity › Mostow Rigidity:laplacian_perturbation_stability | rank 5/307 | 0.9999 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources