L-System (Dragon Curve)
symbolic-dynamics · 37 views
symbolic-dynamicssymbolic
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 additionally detects Multi-Scale Wasserstein:w_max_ratio.
What standard analysis sees
tail heaviness0.01
asymmetry0.40
occupancy0.06
short-range corr0.29
long-range memory0.08
spectral colour0.76
periodicity0.84
complexity0.36
time-irreversibility0.48
volatility clustering0.23
multifractality0.06
dimensionality0.54
nonstationarity0.03
What the atlas adds
Multi-Scale Wasserstein:w_max_ratio+2.3z
scale-coherent dispersion mismatch (max/min Wasserstein across scales)
Atlas-extreme metrics the standard bank can’t predict for this source
Gottwald-Melbourne:k_variance | +5.5z | bank-miss 1.4σ |
Nonstationarity:change_quantiles_mid | +4.0z | bank-miss 1.1σ |
Lorentzian:crossing_density | +3.4z | bank-miss 1.5σ |
Spherical S²:angular_spread | +3.4z | bank-miss 1.5σ |
Nonstationarity:dynamic_coupling | +3.2z | bank-miss 1.5σ |
Modular Residue:occupancy_entropy | -2.4z | bank-miss 1.7σ |
Higher-Order Statistics:bicoherence_max | +2.2z | bank-miss 1.6σ |
Composition
dtypefloat64
range[0, 1]
unique values2 / 16384
mean ± std0.5 ± 0.5
Binary sequence — two distinct symbols.
Render Gallery
.png)
Native > phase_plotraw
.png)
Native > timeseriesraw
.png)
Native > triple_latticeraw
.png)
Boltzmann > lag_map
.png)
Boltzmann > spin_grid
.png)
Cayley > default
.png)
Chladni > free_plate_nodal
.png)
Chladni > plate_bottom
.png)
Chladni > plate_top
_(centered)/signed_log_z/L-System_(Dragon_Curve).png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/L-System_(Dragon_Curve).png)
Heisenberg (Nil) (centered) > xy_path
.png)
Hodge–Laplacian > default
/barcode/L-System_(Dragon_Curve).png)
Inflation (Substitution) > barcode
/d_curve/L-System_(Dragon_Curve).png)
Inflation (Substitution) > d_curve
.png)
Information Theory > default
.png)
Julia Set > escape_histogram
.png)
Klein Bottle > default
.png)
Laplacian > default
.png)
Logarithmic Spiral > default
.png)
Möbius-S³ > mobius_cylinder
.png)
Möbius-S³ > s2_base_map
.png)
Ordinal Partition > default
/phi_spectrum/L-System_(Dragon_Curve).png)
Penrose (Quasicrystal) > phi_spectrum
.png)
Persistent Homology > barcode
.png)
Persistent Homology > h1_diagram
.png)
Predictability > default
.png)
Recurrence Quantification > default
.png)
Spectral Analysis > default
.png)
Spectral Graph > default
.png)
Spirograph > mode_spectrum
.png)
Spirograph > phasor_trajectory
.png)
Symplectic > flux_grid
.png)
Symplectic > phase_space
/default/L-System_(Dragon_Curve).png)
Ulam Spiral (Sacks) > default
/default/L-System_(Dragon_Curve).png)
Ulam Spiral (Square) > default
.png)
Visibility Graph > default
.png)
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Kolakoski Sequence | 4.28 | |
| Fibonacci Word | 4.30 | |
| Thue-Morse | 4.38 |
Which Geometries Light Up
Ammann-Beenker (Octagonal) › Ammann-Beenker (Octagonal):convergent_profile | rank 304/307 | -0.1522 |
Boltzmann › Boltzmann:dominant_lag | rank 1/307 | 1024.0000 |
Boltzmann › Boltzmann:spectral_gap_J | rank 2/307 | 0.9998 |
Boltzmann › Boltzmann:nn_dominance | rank 306/307 | 0.0002 |
Cantor Set › Cantor Set:bit_plane_autocorrelation | rank 307/307 | 0.0001 |
Catch24 › Catch24:DN_Spread_Std | rank 3/307 | 0.5000 |
Gottwald-Melbourne › Gottwald-Melbourne:k_variance | rank 1/307 | 0.8832 |
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):area_length_ratio | rank 305/307 | 0.0000 |
Higher-Order Statistics › Higher-Order Statistics:bicoherence_max | rank 5/307 | 0.9999 |
Higher-Order Statistics › Higher-Order Statistics:skew_mean | rank 303/307 | 0.0001 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):curvature_structure | rank 304/307 | 1.1201 |
Lorentzian › Lorentzian:crossing_density | rank 1/307 | 0.7500 |
Mostow Rigidity › Mostow Rigidity:laplacian_perturbation_stability | rank 4/307 | 1.0000 |
Navier-Stokes › Navier-Stokes:ess_rescaling_gain | rank 304/307 | 0.0000 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 3/307 | 0.1037 |
Projective ℙ² › Projective ℙ²:mean_distance | rank 5/307 | 0.3646 |
Spectral Analysis › Spectral Analysis:spectral_r2 | rank 305/307 | 0.0000 |
Spherical S² › Spherical S²:angular_spread | rank 2/307 | 1.5708 |
Spherical S² › Spherical S²:hemisphere_balance | rank 4/307 | 0.9999 |
Spherical S² › Spherical S²:concentration | rank 306/307 | 0.0001 |
Symplectic › Symplectic:windowed_area_cv | rank 303/307 | 0.0325 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):sphere_concentration | rank 306/307 | 0.0005 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources