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.
- Jacobi Algorithm
- Jacobian
- Jacobian Conjecture
- Jacobian Curve
- Jacobian Determinant
- Jacobi-Anger Expansion
- Jacobian Group
- Jacobi Differential Equation
- Jacobi Differential Equation (Calculus of Variations)
- Jacobi Elliptic Functions
- Jacobi Function of the First Kind
- Jacobi Function of the Second Kind
- Jacobi-Gauss Quadrature
- Jacobi Identities
- Jacobi Matrix
- Jacobi Method
- Jacobi Polynomial
- Jacobi Quadrature
- Jacobi Rotation Matrix
- Jacobi's Curvature Theorem
- Jacobi's Determinant Identity
- Jacobi's Imaginary Transformation
- Jacobi's Theorem
- Jacobi Symbol
- Jacobi Tensor