Fractal Type
Generation Parameters
Box-Counting Dimension
Visualization
Actions
Dimension Analysis
Calculated Dimension
-
D = lim(log(N(ε))/log(1/ε)) as ε→0
Theoretical Dimension
-
Known value for this fractal
Error
-
|calculated - theoretical|
Boxes Analyzed
-
Total boxes across all scales
R² Value
-
Fit quality of log-log regression
Rendering Time
-
Time to generate fractal
Log-Log Plot: log(N) vs log(1/ε)
Data Points
Best Fit Line
Box-Counting Dimension Formula
D = limε→0 (log(N(ε)) / log(1/ε))
Where N(ε) is the number of boxes of size ε needed to cover the fractal
Connection to Constraint Theory
Fractals emerge from simple geometric constraints applied recursively. The non-integer dimension reflects how the constraint system fills space more efficiently than a 1D line but less completely than a 2D area.