L-System (Dragon Curve)

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exotic

What It Is

Dragon curve L-system (F→F+G, G→F-G) --- the turn sequence is the regular paper-folding sequence, a non-periodic deterministic binary sequence with fractal spectral measure

Interpretation

Standard analysis sees: bounded / light-tailed; few distinct values; anti-persistent; monofractal; stationary. The atlas finds no named structure, but the source is distinctively extreme on Persistent Homology:max_h1_lifetime (+4.3z) — beyond what the standard bank predicts for it.

What standard analysis sees

tail heaviness0.01

asymmetry0.40

occupancy0.06

short-range corr0.29

long-range memory0.08

spectral colour0.76

periodicity0.84

complexity0.37

time-irreversibility0.49

volatility clustering0.23

multifractality0.06

dimensionality0.54

nonstationarity0.03

What the atlas adds

Atlas-extreme metrics the standard bank can’t predict for this source

`Persistent Homology:max_h1_lifetime`	+4.3z	bank-miss 1.3σ
`Nonstationarity:change_quantiles_mid`	+4.0z	bank-miss 1.7σ
`Nonstationarity:dynamic_coupling`	+3.4z	bank-miss 1.1σ
`Lorentzian:crossing_density`	+3.4z	bank-miss 1.3σ
`Spherical S²:angular_spread`	+3.4z	bank-miss 1.1σ
`Modular Residue:occupancy_entropy`	-2.4z	bank-miss 1.3σ
`Higher-Order Statistics:bicoherence_max`	+2.2z	bank-miss 1.1σ

Composition

dtypefloat64

range[0, 1]

unique values2 / 16384

mean ± std0.5 ± 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 > plate_bottom

Chladni > plate_top

Heisenberg (Nil) (centered) > signed_log_z

Heisenberg (Nil) (centered) > xy_path

Hodge–Laplacian > default

Inflation (Substitution) > barcode

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

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

Ulam Spiral (Sacks) > default

Ulam Spiral (Square) > default

Visibility Graph > default

Wavelet Cascade > default

Atlas Position

Nearest neighbor	Distance
Kolakoski Sequence	4.44
Thue-Morse	4.59
Fibonacci Word	4.66

Open in Atlas →

Which Geometries Light Up

Ammann-Beenker (Octagonal) › `Ammann-Beenker (Octagonal):convergent_profile`	rank 296/298	-0.1716
Boltzmann › `Boltzmann:dominant_lag`	rank 2/298	1024.0000
Boltzmann › `Boltzmann:spectral_gap_J`	rank 2/298	0.9998
Boltzmann › `Boltzmann:nn_dominance`	rank 297/298	0.0002
Cantor Set › `Cantor Set:bit_plane_autocorrelation`	rank 298/298	0.0001
Catch24 › `Catch24:DN_Spread_Std`	rank 3/298	0.5000
Gottwald-Melbourne › `Gottwald-Melbourne:k_variance`	rank 1/298	0.8836
Heisenberg (Nil) (centered) › `Heisenberg (Nil) (centered):area_length_ratio`	rank 296/298	0.0000
Higher-Order Statistics › `Higher-Order Statistics:bicoherence_max`	rank 5/298	0.9998
Higher-Order Statistics › `Higher-Order Statistics:skew_mean`	rank 294/298	0.0001
Hyperbolic (Poincaré) › `Hyperbolic (Poincaré):curvature_structure`	rank 295/298	1.1201
Lorentzian › `Lorentzian:crossing_density`	rank 1/298	0.7500
Mostow Rigidity › `Mostow Rigidity:spectral_rigidity`	rank 3/298	1.0000
Navier-Stokes › `Navier-Stokes:ess_quality`	rank 295/298	0.0000
Nonstationarity › `Nonstationarity:dynamic_coupling`	rank 3/298	7.9557
Ordinal Partition › `Ordinal Partition:markov_mixing`	rank 3/298	0.9999
Ordinal Partition › `Ordinal Partition:statistical_complexity`	rank 3/298	0.1037
Projective ℙ² › `Projective ℙ²:mean_distance`	rank 3/298	0.3645
Sol (Thurston) › `Sol (Thurston):path_length`	rank 294/298	97010.8135
Spectral Analysis › `Spectral Analysis:spectral_r2`	rank 296/298	0.0000
Spherical S² › `Spherical S²:angular_spread`	rank 2/298	1.5708
Spherical S² › `Spherical S²:hemisphere_balance`	rank 3/298	0.9999
Spherical S² › `Spherical S²:concentration`	rank 297/298	0.0001
Symplectic › `Symplectic:windowed_area_cv`	rank 296/298	0.0319
S² × ℝ (Thurston) › `S² × ℝ (Thurston):sphere_concentration`	rank 297/298	0.0006

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