From Math Images
I'd move the "infinite and self similar" section up above the one about length.
I also think to address Chris's comment about a mouse over, you should just link to Field:Fractals
Very cool fractal. Great opening section.
Length: You are reducing the length by 1/3, not 2/3. You are multiplying the length by 2/3. I assume you mean “This is apparent…”
When you write that the “total length of a Cantor set is 0,” I get it on one level but not on another. I get that it approaches 0, but what about all the lengths that have gone before? L(1) = 2/3 L(0). How is it that the 2/3 is not included in the total length?
Self Similar and Infinite; Would it help the reader to have the word “fractal” in green with a mouseover?
I assume that “A More Mathematical Explanation” is incomplete.
In 1st remarks should "fractal" be a link? Also mention there that the picture's relation to the cantor set will be seen below (it's a great picture!)
In Length before the formula with lim L0, why not have a line that has length after n iterations
- L0 = , L1 = ,
and list a whole bunch (till you get tired)?
Maybe "This is because we do not remove endpoints when we remove the middle thirds" and forget about open sets. Again you could show some infinite string easily seen to be in the set, 1/3, 1/9, ... or whatever.
I'd like the following to be a bit different: "By being infinitely self-similar, the Cantor set is a fractal be [you mean BY and you need a ref!]definition" and I'm not happy with infinite complexity -- infinite is a word to avoid unless it's part of a process, like infinitely many iterations.
Can you please show the very end today? I want to go over some ideas on what we do with this.
Most changes have been made. What specifically do you want changed with "By being infinitely self-similar, the Cantor set is a fractal by?"