Forest Fire
exotic · 36 views
exotic
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 finds no named structure, but the source is distinctively extreme on Higher-Order Statistics:c3_energy (+6.5z) — beyond what the standard bank predicts for it. It sits beside Devil's Staircase in the atlas (standard-bank rank 80) — a neighbor conventional features miss.
What standard analysis sees
tail heaviness0.97
asymmetry0.00
occupancy0.11
short-range corr0.69
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
Atlas-extreme metrics the standard bank can’t predict for this source
Higher-Order Statistics:c3_energy | +6.5z | bank-miss 1.0σ |
Visibility Graph:avg_clustering_coeff | -5.6z | bank-miss 2.8σ |
Zariski:heyting_gap | +5.5z | bank-miss 1.1σ |
S² × ℝ (Thurston):height_drift | +4.6z | bank-miss 1.1σ |
D4 Triality:edge_ortho_polarity | -4.4z | bank-miss 1.1σ |
Navier-Stokes:cascade_asymmetry | -4.2z | bank-miss 1.4σ |
Piecewise-Linear:envelope_area | +3.8z | bank-miss 3.5σ |
SL(2,ℝ) (Thurston):lyapunov_exponent | +3.1z | bank-miss 2.9σ |
Composition
dtypefloat64
range[0, 500]
unique values307 / 16384
mean ± std494 ± 40
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Forest_Fire.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Forest_Fire.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Forest_Fire.png)
Inflation (Substitution) > barcode
/d_curve/Forest_Fire.png)
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
/phi_spectrum/Forest_Fire.png)
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
/default/Forest_Fire.png)
Ulam Spiral (Sacks) > default
/default/Forest_Fire.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| ECG Fusion | 5.52 | cross-domain |
| Devil's Staircase | 5.63 | |
| BTC Volatility | 5.64 | cross-domain |
Which Geometries Light Up
Boltzmann › Boltzmann:spectral_gap_J | rank 1/298 | 1.0000 |
Boltzmann › Boltzmann:coupling_strength | rank 298/298 | 0.0000 |
Boltzmann › Boltzmann:coupling_temporal_variance | rank 298/298 | 0.0000 |
Boltzmann › Boltzmann:nn_dominance | rank 298/298 | 0.0000 |
Catch24 › Catch24:DN_Mean | rank 1/298 | 0.9781 |
Catch24 › Catch24:SB_TransitionMatrix_3ac_sumdiagcov | rank 1/298 | 0.3333 |
Catch24 › Catch24:SB_MotifThree_quantile_hh | rank 298/298 | 0.0000 |
Chladni › Chladni:temporal_burstiness | rank 3/298 | 0.6537 |
Chladni › Chladni:nodal_gap_ratio | rank 295/298 | 0.2037 |
H4 600-Cell › H4 600-Cell:lattice_closure | rank 4/298 | 0.9981 |
Higher-Order Statistics › Higher-Order Statistics:c3_energy | rank 2/298 | 3.4028 |
Higher-Order Statistics › Higher-Order Statistics:kurt_max | rank 4/298 | 6.7125 |
Higher-Order Statistics › Higher-Order Statistics:perm_entropy | rank 298/298 | 0.0085 |
Hodge–Laplacian › Hodge–Laplacian:source_fraction | rank 295/298 | 0.1198 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):depth_height_corr | rank 1/298 | 0.6801 |
Inflation (Substitution) › Inflation (Substitution):discrepancy | rank 297/298 | 0.0000 |
Möbius-S³ › Möbius-S³:phase_profile_deviation | rank 3/298 | 0.7161 |
Navier-Stokes › Navier-Stokes:cascade_asymmetry | rank 295/298 | -0.9625 |
Nonstationarity › Nonstationarity:vol_of_vol | rank 4/298 | 2.4736 |
Piecewise-Linear › Piecewise-Linear:envelope_area | rank 1/298 | 15968.9621 |
Predictability › Predictability:sample_entropy | rank 295/298 | 0.0226 |
S² × ℝ (Thurston) › S² × ℝ (Thurston):height_drift | rank 3/298 | 0.8272 |
Time Reversibility › Time Reversibility:increment_skewness_max | rank 4/298 | 1.0000 |
Visibility Graph › Visibility Graph:avg_clustering_coeff | rank 297/298 | 0.0541 |
Wavelet Cascade › Wavelet Cascade:intermittency_slope | rank 297/298 | -2.7504 |
Zariski › Zariski:heyting_gap | rank 1/298 | 1.0000 |
Zipf–Mandelbrot (16-bit) › Zipf–Mandelbrot (16-bit):gini_coefficient | rank 5/298 | 0.9512 |
Zipf–Mandelbrot (8-bit) › Zipf–Mandelbrot (8-bit):gini_coefficient | rank 5/298 | 0.9519 |
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