Kinda like the I Ching..........an ancient Chinese text.........halving lines......breaking lines..........kinda like sieving...............................2 is a simple sieve..........the 1st one..........the 1st sieve is 2........words into math......1/2................
Cantor Dust
  Cantor dust is a fractal that can be constructed using string rewriting beginning with a cell [0] and iterating the rules
![{0->[0 0 0; 0 0 0; 0 0 0],1->[1 0 1; 0 0 0; 1 0 1]}.](http://mathworld.wolfram.com/images/equations/CantorDust/NumberedEquation1.gif) |
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The  th iteration of Cantor dust is implemented in the Wolfram Language as CantorMesh[ n, 2].
Let  be the number of black boxes,  the length of a side of a box, and  the fractional area of black boxes after the  th iteration, then
The number of black squares after  , 1, 2, ... iterations is therefore 1, 4, 16, 64, 256, 1024, 4096, 16384, ... (OEIS A000302). The capacity dimension is therefore
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