At the critical threshold, burn patterns exhibit fractal geometry - self-similar at all scales.
Use box-counting method to estimate fractal dimension. D â 91/48 â 1.896 for 2D percolation.
Below critical: D â 1 (linear). Above: D â 2 (filled). At critical: fractal!
Burn Pattern
Box-Counting Analysis
Fractal Dimension:-
Burned Cells:-
Reached Edge:-
Theory:
2D Percolation at p_c:
D_fractal â 91/48 â 1.896
Box-counting: log(N) vs log(1/ε)