Logistic r=3.5 (Period-4)

iterated-maps · 37 views
iterated-mapsperiodic

What It Is

Logistic map in period-4 --- four-value cycle after the second bifurcation, output concentrates on four narrow bands

Interpretation

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

What standard analysis sees
tail heaviness0.05
asymmetry0.20
occupancy0.17
short-range corr0.00
long-range memory0.00
spectral colour0.27
periodicity0.99
complexity0.21
time-irreversibility0.21
volatility clustering0.23
multifractality0.01
dimensionality0.45
nonstationarity0.00
What the atlas adds
Nonstationarity:adf_pvalue+5.9z
unit-root nonstationarity (ADF cannot reject random-walk null)
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
Heisenberg (Nil) (centered):xy_spread+5.5zbank-miss 1.2σ
2-adic:valuation_transition_predictability+3.0zbank-miss 1.9σ
Boltzmann:spectral_gap_J-2.7zbank-miss 1.4σ
2-adic:multiscale_markov_predictability+2.2zbank-miss 1.3σ
Klein Bottle:rank_deficit_max+2.0zbank-miss 2.0σ

Composition

dtypefloat64
range[0.3828, 0.875]
unique values4 / 16384
mean ± std0.646 ± 0.209

Fixed alphabet — only 4 distinct symbols across 16384 samples.

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
Sine Map (Feigenbaum)4.02
Logistic Edge-of-Chaos4.16
Logistic r=3.2 (Period-2)4.57

Open in Atlas →

Which Geometries Light Up

2-adic › 2-adic:valuation_transition_predictabilityrank 1/3061.0000
2-adic › 2-adic:multiscale_markov_predictabilityrank 2/3061.0000
2-adic › 2-adic:valuation_spectral_concentrationrank 3/3060.9015
Ammann-Beenker (Octagonal) › Ammann-Beenker (Octagonal):convergent_profilerank 306/306-0.2021
Attractor Reconstruction › Attractor Reconstruction:d2_saturationrank 1/3060.9974
Attractor Reconstruction › Attractor Reconstruction:filling_ratiorank 305/3060.0020
Catch24 › Catch24:FC_LocalSimple_mean3_stderrrank 1/3061.3333
Catch24 › Catch24:CO_f1ecacrank 305/3060.3236
Catch24 › Catch24:SP_Summaries_welch_rect_area_5_1rank 305/3060.0000
Chladni › Chladni:modal_nodal_cascaderank 4/3062.0377
Chladni › Chladni:plate_low_mode_fractionrank 302/3060.0235
D4 Triality › D4 Triality:gram_consistencyrank 304/3060.0000
E8 Lattice › E8 Lattice:std_profilerank 306/3060.0000
G2 Root System › G2 Root System:pair_angle_kurtosisrank 306/306-2.0000
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):area_length_ratiorank 2/3060.3899
Heisenberg (Nil) (centered) › Heisenberg (Nil) (centered):xy_spreadrank 2/3064618.9876
Higher-Order Statistics › Higher-Order Statistics:skew_meanrank 303/3060.0000
Higher-Order Statistics › Higher-Order Statistics:bicoherence_maxrank 306/3060.0000
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):temporal_variancerank 305/3060.0000
Hyperbolic (Poincaré) › Hyperbolic (Poincaré):curvature_structurerank 306/3061.0000
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_step_dispersionrank 2/3068.2805
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_triangle_arearank 2/3062.3647
Hölder Regularity › Hölder Regularity:holder_meanrank 304/306-1.8938
Information Theory › Information Theory:compression_ratiorank 302/3060.0029
Julia Set › Julia Set:potential_smoothnessrank 2/3067001.6005
Julia Set › Julia Set:potential_variancerank 2/30646322561.8590
Julia Set › Julia Set:escape_entropyrank 304/3062.5856
Klein Bottle › Klein Bottle:wht_spectral_kurtosisrank 2/3069.4294
Klein Bottle › Klein Bottle:linear_complexityrank 302/3060.0112
Laplacian › Laplacian:biharmonic_ratiorank 3/30615.8541
Lorentzian › Lorentzian:spacelike_fractionrank 5/3060.1758
Moiré › Moiré:moire_integer_excessrank 1/3060.6457
Moiré › Moiré:moire_max_coherencerank 2/3061.0000
Moiré › Moiré:moire_dilation_entropyrank 304/3061.3905
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_finerank 304/3060.0000
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_stdrank 304/3060.0000
Multi-Scale Wasserstein › Multi-Scale Wasserstein:w_meanrank 305/3060.0000
Nonstationarity › Nonstationarity:adf_pvaluerank 2/3060.9585
Nonstationarity › Nonstationarity:change_quantiles_midrank 5/3060.6625
Nonstationarity › Nonstationarity:dynamic_couplingrank 305/3060.0000
Nonstationarity › Nonstationarity:metric_volatilityrank 305/3060.0000
Nonstationarity › Nonstationarity:trajectory_dimrank 305/3060.0000
Nonstationarity › Nonstationarity:vol_of_volrank 305/3060.0000
Sol (Thurston) › Sol (Thurston):path_lengthrank 3/30631729860.1845
Spectral Analysis › Spectral Analysis:spectral_peakednessrank 2/3060.9991
Spectral Analysis › Spectral Analysis:spectral_r2rank 306/3060.0000
Spherical S² › Spherical S²:angular_spreadrank 305/3060.0000
Spherical S² › Spherical S²:hemisphere_balancerank 306/3060.0000
S² × ℝ (Thurston) › S² × ℝ (Thurston):great_circle_dispersionrank 2/3062.6714
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):gini_coefficientrank 304/3060.0000
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):gini_coefficientrank 303/3060.0000
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