Rule 110
symbolic-dynamics · 37 views
symbolic-dynamicssymbolic
What It Is
Wolfram Rule 110 center column --- proven Turing-complete, the simplest known universal computer. Supports gliders and localized structures like a 1D Game of Life
Interpretation
Standard analysis sees: bounded / light-tailed; few distinct values. The atlas finds no named structure, but the source is distinctively extreme on Nonstationarity:regime_persistence (+4.5z) — beyond what the standard bank predicts for it. It sits beside Collatz Parity in the atlas (standard-bank rank 42) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.03
asymmetry0.26
occupancy0.06
short-range corr0.38
long-range memory0.56
spectral colour0.57
periodicity0.50
complexity0.36
time-irreversibility0.51
volatility clustering0.34
multifractality0.83
dimensionality0.63
nonstationarity0.38
What the atlas adds
Atlas-extreme metrics the standard bank can’t predict for this source
Nonstationarity:regime_persistence | +4.5z | bank-miss 1.8σ |
H² × ℝ (Thurston):hyperbolic_step_dispersion | +2.7z | bank-miss 2.0σ |
Modular Residue:occupancy_entropy | -2.3z | bank-miss 1.1σ |
Sol (Thurston):integrated_walk_smoothness | -2.2z | bank-miss 2.0σ |
Lorentzian:crossing_density | +2.2z | bank-miss 1.0σ |
Predictability:entropy_decay_rate | -2.1z | bank-miss 2.2σ |
Composition
dtypefloat64
range[0, 1]
unique values2 / 16384
mean ± std0.604 ± 0.489
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/Rule_110.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Rule_110.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Rule_110.png)
Inflation (Substitution) > barcode
/d_curve/Rule_110.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/Rule_110.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/Rule_110.png)
Ulam Spiral (Sacks) > default
/default/Rule_110.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Symbolic Henon | 4.27 | cross-origin |
| Collatz Parity | 4.37 | cross-origin |
| Symbolic Lorenz | 4.55 | cross-origin |
Which Geometries Light Up
Boltzmann › Boltzmann:spectral_gap_J | rank 4/306 | 0.9952 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_step_dispersion | rank 5/306 | 7.6158 |
Lorentzian › Lorentzian:crossing_density | rank 5/306 | 0.5593 |
Mostow Rigidity › Mostow Rigidity:distance_rigidity | rank 5/306 | 0.9839 |
Nonstationarity › Nonstationarity:regime_persistence | rank 5/306 | 0.7400 |
Nonstationarity › Nonstationarity:metric_volatility | rank 302/306 | 0.3840 |
Wavelet Cascade › Wavelet Cascade:coarse_scale_kurtosis_slope | rank 5/306 | 0.7520 |
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources