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 finds no named structure, but the source is distinctively extreme on Gottwald-Melbourne:k_variance (+5.4z) — beyond what the standard bank predicts for it.
What standard analysis sees
tail heaviness0.00
asymmetry0.41
occupancy0.08
short-range corr0.31
long-range memory0.08
spectral colour0.76
periodicity0.83
complexity0.37
time-irreversibility0.51
volatility clustering0.22
multifractality0.07
dimensionality0.56
nonstationarity0.03
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Gottwald-Melbourne:k_variance | +5.4z | bank-miss 1.5σ |
Nonstationarity:change_quantiles_mid | +3.7z | bank-miss 1.1σ |
Lorentzian:crossing_density | +3.3z | bank-miss 1.5σ |
Spherical S²:angular_spread | +3.1z | bank-miss 1.6σ |
Nonstationarity:dynamic_coupling | +2.9z | bank-miss 1.0σ |
Spirograph:angular_order | +2.6z | bank-miss 1.3σ |
Modular Residue:occupancy_entropy | -2.3z | bank-miss 1.7σ |
Composition
dtypefloat64
range[0, 1]
unique values2 / 16384
mean ± std0.5 ± 0.5
Binary sequence — two distinct symbols.
Render Gallery
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Native > phase_plotraw
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Native > timeseriesraw
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Native > triple_latticeraw
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Boltzmann > lag_map
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Boltzmann > spin_grid
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Cayley > default
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Chladni > free_plate_nodal
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Chladni > plate_bottom
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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
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Hodge–Laplacian > default
/barcode/L-System_(Dragon_Curve).png)
Inflation (Substitution) > barcode
/d_curve/L-System_(Dragon_Curve).png)
Inflation (Substitution) > d_curve
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Information Theory > default
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Julia Set > escape_histogram
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Klein Bottle > default
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Laplacian > default
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Logarithmic Spiral > default
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Möbius-S³ > mobius_cylinder
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Möbius-S³ > s2_base_map
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Ordinal Partition > default
/phi_spectrum/L-System_(Dragon_Curve).png)
Penrose (Quasicrystal) > phi_spectrum
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Persistent Homology > barcode
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Persistent Homology > h1_diagram
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Predictability > default
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Recurrence Quantification > default
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Spectral Analysis > default
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Spectral Graph > default
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Spirograph > mode_spectrum
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Spirograph > phasor_trajectory
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Symplectic > flux_grid
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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
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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 303/306 | -0.1522 |
Boltzmann › Boltzmann:dominant_lag | rank 1/306 | 1024.0000 |
Boltzmann › Boltzmann:spectral_gap_J | rank 2/306 | 0.9998 |
Boltzmann › Boltzmann:nn_dominance | rank 305/306 | 0.0002 |
Cantor Set › Cantor Set:bit_plane_autocorrelation | rank 306/306 | 0.0001 |
Catch24 › Catch24:DN_Spread_Std | rank 3/306 | 0.5000 |
Gottwald-Melbourne › Gottwald-Melbourne:k_variance | rank 1/306 | 0.8832 |
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):area_length_ratio | rank 304/306 | 0.0000 |
Higher-Order Statistics › Higher-Order Statistics:bicoherence_max | rank 5/306 | 0.9999 |
Higher-Order Statistics › Higher-Order Statistics:skew_mean | rank 302/306 | 0.0001 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):curvature_structure | rank 303/306 | 1.1201 |
Lorentzian › Lorentzian:crossing_density | rank 1/306 | 0.7500 |
Mostow Rigidity › Mostow Rigidity:laplacian_perturbation_stability | rank 4/306 | 1.0000 |
Navier-Stokes › Navier-Stokes:ess_rescaling_gain | rank 303/306 | 0.0000 |
Ordinal Partition › Ordinal Partition:statistical_complexity | rank 3/306 | 0.1037 |
Projective ℙ² › Projective ℙ²:mean_distance | rank 5/306 | 0.3646 |
Spectral Analysis › Spectral Analysis:spectral_r2 | rank 304/306 | 0.0000 |
Spherical S² › Spherical S²:angular_spread | rank 2/306 | 1.5708 |
Spherical S² › Spherical S²:hemisphere_balance | rank 4/306 | 0.9999 |
Spherical S² › Spherical S²:concentration | rank 305/306 | 0.0001 |
Symplectic › Symplectic:windowed_area_cv | rank 302/306 | 0.0325 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):sphere_concentration | rank 305/306 | 0.0005 |
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