Sine Map (Feigenbaum)

What It Is

Sine map x(n+1) = r*sin(pi*x) at r=0.8640 --- near the period-doubling accumulation for this functional form (the cascade accumulates just above r≈0.8641; sustained chaos appears near r≈0.867, with periodic windows between). Functionally distinct from the logistic map but in the SAME Feigenbaum universality class (quadratic-tip, z=2, delta=4.6692). Tests whether the atlas rediscovers period-doubling universality unsupervised: should cluster tightly with Logistic Edge-of-Chaos despite the different functional form

Interpretation

Standard analysis sees: bounded / light-tailed; anti-correlated (alternating); anti-persistent; strongly periodic; monofractal; low-dimensional; stationary. The atlas additionally detects Time Reversibility:ordinal_reversal_distance.

Composition

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

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 →

Which Geometries Light Up