A beautiful aspect of Pascal's triangle modulo 2 is that the `pattern' inside any triangle of 1's is similar in design to that of any subtriangle, though larger in size. If we extend Pascal's triangle to infinitely many rows, and reduce the scale of our picture in half each time that we double the number of rows, then the resulting design is called self--similar -- that is, our picture can be reproduced by taking any subtriangle and magnifying it. Such an approach to Pascal's triangle is taken in [22]; and many examples of self--similarity have been investigated by Mandelbrot [16].
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