Tribonacci Word

What It Is

Cubic-Pisot Sturmian-like: substitution a→ab, b→ac, c→a. Substitution matrix [[1,1,0],[1,0,1],[1,0,0]] has eigenvalue Tribonacci constant ≈1.839 (real root of x³=x²+x+1). Ternary alphabet, cubic algebraic ratio --- a degree-3 Pisot contrast class against degree-2 Fibonacci/Pell.

Interpretation

Standard analysis sees: few distinct values; anti-correlated (alternating); anti-persistent; blue spectrum (high-frequency power); strongly periodic; homoskedastic; monofractal; stationary. The atlas finds no named structure, but the source is distinctively extreme on Julia Set:potential_variance (+4.8z) — beyond what the standard bank predicts for it.

Composition

Fixed alphabet — only 3 distinct symbols across 16384 samples.

Render Gallery

Native > phase_plotraw

Native > timeseriesraw

Native > triple_latticeraw

Boltzmann > lag_map

Boltzmann > spin_grid

Cayley > default

Chladni > plate_bottom

Chladni > plate_top

Heisenberg (Nil) (centered) > signed_log_z

Heisenberg (Nil) (centered) > xy_path

Hodge–Laplacian > default

Inflation (Substitution) > barcode

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

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

Ulam Spiral (Sacks) > default

Ulam Spiral (Square) > default

Visibility Graph > default

Wavelet Cascade > default

Atlas Position

Open in Atlas →

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