Quartic Map (Feigenbaum)

What It Is

Quartic map x(n+1) = 1 - r*x^4 at r=1.5949 --- accumulation of the period-doubling cascade for the z=4 family. DIFFERENT Feigenbaum universality class from logistic/sine (quartic-tip, delta=7.2847). Tests whether the atlas distinguishes universality classes: should be near Logistic Edge-of-Chaos and Sine Map (Feigenbaum) but discernibly separate

Interpretation

Standard analysis sees: bounded / light-tailed; left-skewed; anti-correlated (alternating); anti-persistent; strongly periodic; monofractal; low-dimensional; stationary. The atlas additionally detects Time Reversibility:ordinal_reversal_distance. It sits beside Logistic r=3.65 (Banded Chaos) in the atlas (standard-bank rank 23) — a neighbor conventional features miss.

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