Box Fractal
A Fractal which can be constructed using String Rewriting by creating a matrix with 3 times as many entries as the current matrix using the rules
Let 
be the number of black boxes, 
the length of aside of a white box, and 
the fractional Area of black boxes after the 
th iteration.
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
The Capacity Dimension is therefore
 | |  | |
|  | (4) |
See also Cantor Dust, Sierpinski Carpet, Sierpinski Sieve
References
Weisstein, E. W. ``Fractals.'' Mathematica notebook Fractal.m.
- Well-Ordering Principle
- Werner Formulas
- Weyl's Criterion
- Weyl Tensor
- Weyrich's Formula
- W-Function
- Wheat and Chessboard Problem
- Wheel
- Wheel Graph
- Wheel Paradox
- Whewell Equation
- Whipple's Transformation
- Whirl
- Whisker Plot
- Whitehead Double
- Whitehead Link
- Whitehead Manifold
- Whitehead's Theorem
- Whitney-Graustein Theorem
- Whitney-Mikhlin Extension Constants
- Whitney Singularity
- Whitney Sum
- Whitney Umbrella
- Whittaker Differential Equation
- Whittaker Function