Cantor's comb

MathematicalPhysicist

Gold Member
does it have other applications in maths?

KLscilevothma

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 )

Besides these 2, I don't know whether it has any other application in math

Integral

Staff Emeritus
Gold Member
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.

MathematicalPhysicist

Gold Member
Originally posted by KL Kam
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 )

Besides these 2, I don't know whether it has any other application in math
how is it used in fractals?

KLscilevothma

Originally posted by loop quantum gravity
how is it used in fractals?
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.

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

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