Forest Fire

self-organized-criticality · 37 views
self-organized-criticalityavalanching

What It Is

Drossel-Schwabl forest fire model --- tree density fluctuates as growth and burns compete

Interpretation

Standard analysis sees: heavy-tailed; left-skewed; few distinct values; low-complexity (predictable, not noise-like); time-irreversible (slow rise, sharp collapse); multifractal; low-dimensional; nonstationary / drifting. The atlas additionally detects Higher-Order Statistics:c3_energy. It sits beside Rainfall (ORD Hourly) in the atlas (standard-bank rank 153) — a neighbor conventional features miss.

What standard analysis sees
tail heaviness0.97
asymmetry0.00
occupancy0.11
short-range corr0.68
long-range memory0.80
spectral colour0.34
periodicity0.40
complexity0.01
time-irreversibility0.01
volatility clustering0.70
multifractality0.93
dimensionality0.02
nonstationarity0.87
What the atlas adds
Higher-Order Statistics:c3_energy+6.0z
third-cumulant burst energy (SOC irreducibility signature)
Atlas-extreme metrics the standard bank can’t predict for this source
Visibility Graph:avg_clustering_coeff-5.9zbank-miss 2.6σ
Zariski:heyting_gap+5.6zbank-miss 1.1σ
D4 Triality:edge_ortho_polarity-4.5zbank-miss 1.4σ
Navier-Stokes:cascade_asymmetry-4.1zbank-miss 2.3σ
Piecewise-Linear:envelope_area+3.7zbank-miss 3.7σ
SL(2,ℝ) (Thurston):lyapunov_exponent+3.1zbank-miss 3.1σ
Inflation (Substitution):return_concentration+2.8zbank-miss 6.7σ
H² × ℝ (Thurston):depth_height_corr+2.8zbank-miss 1.1σ

Composition

dtypefloat64
range[0, 500]
unique values307 / 16384
mean ± std494 ± 40

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
Rainfall (ORD Hourly)5.13cross-origin
Devil's Staircase5.14cross-origin
ECG Fusion5.25cross-origin

Open in Atlas →

Which Geometries Light Up

Boltzmann › Boltzmann:spectral_gap_Jrank 1/3071.0000
Boltzmann › Boltzmann:coupling_temporal_variancerank 307/3070.0000
Boltzmann › Boltzmann:nn_dominancerank 307/3070.0000
Catch24 › Catch24:DN_Meanrank 1/3070.9799
Catch24 › Catch24:SB_TransitionMatrix_3ac_sumdiagcovrank 1/3070.3333
Catch24 › Catch24:SB_MotifThree_quantile_hhrank 307/3070.0000
Chladni › Chladni:temporal_burstinessrank 3/3070.6616
Chladni › Chladni:nodal_gap_ratiorank 304/3070.1968
H4 600-Cell › H4 600-Cell:lattice_closurerank 4/3070.9980
Higher-Order Statistics › Higher-Order Statistics:c3_energyrank 2/3073.4088
Higher-Order Statistics › Higher-Order Statistics:kurt_maxrank 5/3076.7116
Higher-Order Statistics › Higher-Order Statistics:perm_entropyrank 307/3070.0084
Hodge–Laplacian › Hodge–Laplacian:source_fractionrank 304/3070.1098
H² × ℝ (Thurston) › H² × ℝ (Thurston):depth_height_corrrank 2/3070.6765
Inflation (Substitution) › Inflation (Substitution):discrepancyrank 306/3070.0000
Möbius-S³ › Möbius-S³:phase_profile_deviationrank 3/3070.7211
Navier-Stokes › Navier-Stokes:cascade_asymmetryrank 304/307-0.9616
Nonstationarity › Nonstationarity:vol_of_volrank 4/3072.4817
Predictability › Predictability:sample_entropyrank 304/3070.0217
S² × ℝ (Thurston) › S² × ℝ (Thurston):height_driftrank 3/3070.8190
Time Reversibility › Time Reversibility:increment_skewness_maxrank 4/3071.0000
Visibility Graph › Visibility Graph:avg_clustering_coeffrank 306/3070.0541
Wavelet Cascade › Wavelet Cascade:coarse_scale_kurtosis_sloperank 306/307-2.7407
Zariski › Zariski:heyting_gaprank 1/3071.0000
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):gini_coefficientrank 4/3070.9537
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):gini_coefficientrank 5/3070.9553
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Structure Atlas — Open Atlas · GitHub