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Cantor's comb

  1. Jul 11, 2003 #1

    MathematicalPhysicist

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    does it have other applications in maths?
     
  2. jcsd
  3. Jul 11, 2003 #2
    After doing some research in google, I found 2 results.
    1) It is used to visualize the Cantor set
    2) It can be put under the topic, fractals (I prefer a 2D fractal to a one-dimension one :wink:)

    Besides these 2, I don't know whether it has any other application in math
     
  4. Jul 11, 2003 #3

    Integral

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    I once did a homework assignment that started with the cantor set and ended with the binary number system. Along the way the equivalance of 1 and .999... or .111... binary fell out.
     
  5. Jul 12, 2003 #4

    MathematicalPhysicist

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    how is it used in fractals?
     
  6. Jul 13, 2003 #5
    The 3 properties of fractals are
    1. Self-similarity
    2. Fractional dimension
    3. Formation by iteration

    For Cantor's Comb, it has property 1. I guess it can be formed by iteration but I'm not sure. Also I'm not sure whether it has fractional dimension. I'm not an expert and I think some mathematicians here can clear it up a bit.
     
  7. Jul 14, 2003 #6
    I'm in no sense an expert or even knowledgable on this issue, but wouldn't it have to have a fractal dimension? It could be 0, which is still a fractal dimension. I can't remember exactly, but I think Cantor's Dust has a fractal dimension between 0 and 1 , and Cantor's box has a fractal dimension of 0.

    Here is a good website I found on fractals, but it dosn't seem to be working at the moment.

    http://library.thinkquest.org/26242...torial/ch4.html
     
    Last edited by a moderator: Apr 20, 2017
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