Cantor Dust
A Fractal which can be constructed using String Rewriting by creating a matrix three times the size ofthe current matrix using the rules
Let 
be the number of black boxes, 
the length of a side of a white box, and 
the fractional Area ofblack boxes after the 
th iteration.
 |  |  | (1) |
 | |  | (2) |
 | |  | (3) |
The Capacity Dimension is therefore
 | |  | |
|  | (4) |
See also Box Fractal, Sierpinski Carpet, Sierpinski Sieve
References
Dickau, R. M. ``Cantor Dust.''http://forum.swarthmore.edu/advanced/robertd/cantor.html.
Ott, E. Chaos in Dynamical Systems. New York: Cambridge University Press, pp. 103-104, 1993.
Weisstein, E. W. ``Fractals.'' Mathematica notebook Fractal.m.
- Anallagmatic Curve
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