Cantor's comb

  • #1
MathematicalPhysicist
Gold Member
4,699
369
does it have other applications in maths?
 

Answers and Replies

  • #2
KLscilevothma
322
0
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
 
  • #3
Integral
Staff Emeritus
Science Advisor
Gold Member
7,253
63
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.
 
  • #4
MathematicalPhysicist
Gold Member
4,699
369
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 :wink:)

Besides these 2, I don't know whether it has any other application in math
how is it used in fractals?
 
  • #5
KLscilevothma
322
0
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.
 
  • #6
On Radioactive Waves
137
0
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:

Suggested for: Cantor's comb

  • Last Post
Replies
3
Views
529
  • Last Post
Replies
22
Views
2K
  • Last Post
Replies
19
Views
1K
Replies
29
Views
3K
Replies
9
Views
1K
Replies
11
Views
844
  • Last Post
Replies
6
Views
413
Replies
2
Views
195
Replies
1
Views
234
  • Last Post
Replies
1
Views
417
Top