Logistic Edge-of-Chaos

iterated-maps · 37 views
iterated-mapschaotic

What It Is

Logistic map at the Feigenbaum point r=3.5699 --- the boundary between order and chaos, where the period-doubling cascade accumulates

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.

What standard analysis sees
tail heaviness0.07
asymmetry0.15
occupancy0.29
short-range corr0.01
long-range memory0.01
spectral colour0.35
periodicity0.99
complexity0.21
time-irreversibility0.19
volatility clustering0.37
multifractality0.03
dimensionality0.04
nonstationarity0.02
What the atlas adds
Time Reversibility:ordinal_reversal_distance+3.1z
time-reversal symmetry breaking via Bandt-Pompe ordinal patterns
Atlas-extreme metrics the standard bank can’t predict for this source
Hyperbolic (Poincaré):curvature_structure+6.7zbank-miss 1.2σ
Multi-Scale Wasserstein:w_slope+5.8zbank-miss 3.1σ
Heisenberg (Nil) (centered):xy_spread+5.4zbank-miss 1.6σ
Boltzmann:spectral_gap_J-2.7zbank-miss 1.3σ
Nonstationarity:variance_trend+2.6zbank-miss 2.1σ
Cayley:growth_exponent-2.1zbank-miss 1.7σ
Cayley:local_linearity+2.0zbank-miss 2.9σ

Composition

dtypefloat64
range[0.3426, 0.8925]
unique values6422 / 16384
mean ± std0.648 ± 0.216

Render Gallery

Native > phase_plot
Native > phase_plotraw
Native > timeseries
Native > timeseriesraw
Native > triple_lattice
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > lag_map
Boltzmann > spin_grid
Boltzmann > spin_grid
Cayley > default
Cayley > default
Chladni > free_plate_nodal
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_bottom
Chladni > plate_top
Chladni > plate_top
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > signed_log_z
Heisenberg (Nil) (centered) > xy_path
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
Hodge–Laplacian > default
Inflation (Substitution) > barcode
Inflation (Substitution) > barcode
Inflation (Substitution) > d_curve
Inflation (Substitution) > d_curve
Information Theory > default
Information Theory > default
Julia Set > escape_histogram
Julia Set > escape_histogram
Klein Bottle > default
Klein Bottle > default
Laplacian > default
Laplacian > default
Logarithmic Spiral > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Möbius-S³ > s2_base_map
Ordinal Partition > default
Ordinal Partition > default
Penrose (Quasicrystal) > phi_spectrum
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > barcode
Persistent Homology > h1_diagram
Persistent Homology > h1_diagram
Predictability > default
Predictability > default
Recurrence Quantification > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Analysis > default
Spectral Graph > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > flux_grid
Symplectic > phase_space
Symplectic > phase_space
Ulam Spiral (Sacks) > default
Ulam Spiral (Sacks) > default
Ulam Spiral (Square) > default
Ulam Spiral (Square) > default
Visibility Graph > default
Visibility Graph > default
Wavelet Cascade > default
Wavelet Cascade > default

Atlas Position

Nearest neighborDistance
Quartic Map (Feigenbaum)2.45
Sine Map (Feigenbaum)3.46
Logistic r=3.5 (Period-4)4.16

Open in Atlas →

Which Geometries Light Up

Catch24 › Catch24:FC_LocalSimple_mean3_stderrrank 4/3061.3315
Catch24 › Catch24:CO_f1ecacrank 303/3060.3308
Cayley › Cayley:growth_exponentrank 306/3060.3907
E8 Lattice › E8 Lattice:std_profilerank 303/3060.1163
H4 600-Cell › H4 600-Cell:edge_walk_fractionrank 3/3060.6687
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):area_length_ratiorank 4/3060.3744
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):xy_spreadrank 4/3064507.4926
Higher-Order Statistics › Higher-Order Statistics:bicoherence_maxrank 3/3061.0000
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):curvature_structurerank 2/3061496.3932
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_triangle_arearank 4/3062.1761
Julia Set › Julia Set:potential_smoothnessrank 4/3066945.6577
Julia Set › Julia Set:potential_variancerank 4/30646092238.5543
Julia Set › Julia Set:escape_entropyrank 302/3062.6039
Lorentzian › Lorentzian:spacelike_fractionrank 2/3060.1824
Moiré › Moiré:moire_integer_excessrank 2/3060.6238
Moiré › Moiré:moire_max_coherencerank 5/3060.9919
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_sloperank 4/3064.6558
Multifractal Spectrum › Multifractal Spectrum:spectrum_widthrank 5/3060.4732
Nonstationarity › Nonstationarity:dynamic_couplingrank 304/3060.9768
Projective ℙ² › Projective ℙ²:cross_ratio_stdrank 1/30645.4487
Sol (Thurston) › Sol (Thurston):path_lengthrank 1/30633301994.5346
Spherical S² › Spherical S²:hemisphere_balancerank 304/3060.0000
S² × ℝ (Thurston) › S² × ℝ (Thurston):great_circle_dispersionrank 4/3062.5529
Wavelet Cascade › Wavelet Cascade:coarse_scale_kurtosis_sloperank 2/3061.4015
Wavelet Cascade › Wavelet Cascade:scale_gini_dispersionrank 4/3060.2944
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