Periodic Word
symbolic-dynamics · 37 views
symbolic-dynamicssymbolic
What It Is
Fixed binary pattern of period 7 (…1010010…) tiled with a random phase per trial. Trivially SOFIC --- finitely many follower sets, bounded factor complexity --- and zero topological entropy. The sofic, zero-entropy pole contrasted against the Sturmian words (Fibonacci / Collatz Cycle / Pell), which are NON-sofic at zero entropy (complexity n+1, infinitely many follower sets). Sanity anchor for the soficity probe: clean separation here confirms the atlas sees the easy end of the soficity gradient.
Composition
dtypeuint8
range[0, 255]
unique values2 / 16384
mean ± std109 ± 126
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/Periodic_Word.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Periodic_Word.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Periodic_Word.png)
Inflation (Substitution) > barcode
/d_curve/Periodic_Word.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/Periodic_Word.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/Periodic_Word.png)
Ulam Spiral (Sacks) > default
/default/Periodic_Word.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Collatz Cycle Word | 3.20 | cross-origin |
| Penrose Substitution | 3.70 | |
| Tribonacci Word | 3.91 |
Which Geometries Light Up
AutoRegressive › AutoRegressive:ar_residual_frac | rank 307/307 | 0.0000 |
Catch24 › Catch24:SP_Summaries_welch_rect_area_5_1 | rank 303/307 | 0.0000 |
Catch24 › Catch24:SC_FluctAnal_2_dfa_50_1_2_logi_prop_r1 | rank 304/307 | 0.1200 |
Catch24 › Catch24:SC_FluctAnal_2_rsrangefit_50_1_logi_prop_r1 | rank 304/307 | 0.1260 |
Chladni › Chladni:modal_nodal_cascade | rank 3/307 | 2.0618 |
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):temporal_variance | rank 1/307 | 19.7630 |
Information Theory › Information Theory:compression_ratio | rank 305/307 | 0.0024 |
Laplacian › Laplacian:cross_scale_curvature_coherence | rank 303/307 | -0.5477 |
Möbius-S³ › Möbius-S³:hopf_fiber_coherence | rank 304/307 | 0.1885 |
Nonstationarity › Nonstationarity:change_quantiles_mid | rank 2/307 | 0.8572 |
Nonstationarity › Nonstationarity:dynamic_coupling | rank 5/307 | 8.3234 |
Projective ℙ² › Projective ℙ²:distance_std | rank 2/307 | 0.2604 |
Projective ℙ² › Projective ℙ²:mean_distance | rank 3/307 | 0.3848 |
Sol (Thurston) › Sol (Thurston):integrated_walk_smoothness | rank 307/307 | -0.2712 |
Symplectic › Symplectic:windowed_area_cv | rank 307/307 | 0.0000 |
Time Reversibility › Time Reversibility:increment_skewness_max | rank 307/307 | 0.0002 |
Visibility Graph › Visibility Graph:assortativity | rank 304/307 | -0.4009 |
Wavelet Cascade › Wavelet Cascade:cascade_coupling | rank 303/307 | -0.3333 |
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