Langton's Ant
symbolic-dynamics · 37 views
symbolic-dynamicssymbolic
What It Is
Classic 2-state Langton's Ant (rule RL) from an EMPTY grid --- observed through the chaotic build-up into the emergent diagonal 'highway' (onset ~10^4 steps), on a grid large enough that the highway never wraps; position folded mod 256 so the highway's linear drift reads as a bounded sawtooth, not a monotone ramp
Interpretation
Standard analysis sees: low-dimensional; nonstationary / drifting. The atlas additionally detects Attractor Reconstruction:lyap_entropy. It sits beside GOES X-Ray Flux in the atlas (standard-bank rank 34) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.42
asymmetry0.61
occupancy0.68
short-range corr0.70
long-range memory0.84
spectral colour0.41
periodicity0.74
complexity0.64
time-irreversibility0.78
volatility clustering0.70
multifractality0.79
dimensionality0.07
nonstationarity0.93
What the atlas adds
Attractor Reconstruction:lyap_entropy+4.2z
Kolmogorov-Sinai entropy production rate (sum of positive λ)
Atlas-extreme metrics the standard bank can’t predict for this source
Nonstationarity:variance_trend | -5.0z | bank-miss 1.4σ |
Chladni:temporal_burstiness | +3.7z | bank-miss 3.3σ |
Marginal:tail_occupancy_r1_5 | +2.7z | bank-miss 2.6σ |
S² × ℝ (Thurston):height_drift | +2.6z | bank-miss 2.1σ |
Nonstationarity:ac1_trend | +2.4z | bank-miss 2.1σ |
Composition
dtypefloat64
range[0, 412.6]
unique values3817 / 16384
mean ± std225 ± 118
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/Langtons_Ant.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Langtons_Ant.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Langtons_Ant.png)
Inflation (Substitution) > barcode
/d_curve/Langtons_Ant.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/Langtons_Ant.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/Langtons_Ant.png)
Ulam Spiral (Sacks) > default
/default/Langtons_Ant.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| GOES X-Ray Flux | 4.72 | cross-origin |
| Stochastic Resetting Walk | 4.72 | cross-origin |
| Ocean Wind (Buoy) | 4.82 | cross-origin |
Which Geometries Light Up
Attractor Reconstruction › Attractor Reconstruction:embedding_divergence_sum | rank 2/306 | 4.1824 |
Attractor Reconstruction › Attractor Reconstruction:lyap_entropy | rank 2/306 | 4.6816 |
Chladni › Chladni:temporal_burstiness | rank 5/306 | 0.5970 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_variance | rank 1/306 | 3.5273 |
Julia Set › Julia Set:potential_smoothness | rank 302/306 | 28.6002 |
Marginal › Marginal:tail_occupancy_r1_5 | rank 3/306 | 0.2472 |
Möbius-S³ › Möbius-S³:phi_return_cv | rank 3/306 | 5.4863 |
Nonstationarity › Nonstationarity:variance_trend | rank 305/306 | -0.5150 |
Wasserstein › Wasserstein:recurrence_distance | rank 3/306 | 0.0975 |
Wasserstein › Wasserstein:transport_variability | rank 4/306 | 0.1355 |
Wasserstein › Wasserstein:distributional_stationarity | rank 304/306 | 0.8075 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources