September 03, 1999 at 17:38:57
1. Why is the length of lines in every fractal with a dimension greater than 1 infinite?
Fractals with fractal dimesion greater than 1 are often called fractal curves. As you should know, fractal curves are formed then following way: take a line segment, substitute it with some shape, then subsitute every line segment with the shape again, and continue these subsitutions an infinite number of times. Every time you make the substitutions is called iteration. With every iteration, you increase the length of the curve some number of times. As the number of iterations approaches infinity, the length will increase infinitely as well.
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